{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":43484,"title":"Integrate Me","description":"Given polynomial, output the integral (with k = 1 for simplicity purposes)\r\n\r\nExample:\r\n\r\ninput = [2 1] % 2x+1\r\noutput = [1 1 1] %x^2 + x + k","description_html":"\u003cp\u003eGiven polynomial, output the integral (with k = 1 for simplicity 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woWee+6///6VK1equCSohRQBuqHbi8xbLBYOatA9agT/DR06VK//3OmGJickgBQB+qPho+xgWNQI0CUmJGgJKQJ0jAkJmkGNAH1jQoIGkCLACAgSpMYJUhEqHGInP4IEeTEYAYZCkCAjBiPAgAgSpMNgBBgTQYJEGIwAIyNIkAWDEWBw/B0S1GcyUSOEHddDkh8TElRGigC4ESSohneMAHgjSFAHgxGAJggSlMZgBKBFBAmKYjAC0BqCBIUwGAHwjSBBCQxGAK6IICG8GIwA+IkgIYwYjAD4jyAhLEgRZMP1kOTHqYMQetQIQACYkBBKpAhAwJiQEDLUCEAwmJAQAqQIQPCYkBAsagQgJJiQEDhSBA0xmUwcaCc5JiQEiBoBCC0mJLQZKQIQDkxIaBtqBCBMmJDgL1IEIKwIEq6ME6QCUABBwhUwGAFQBkFCqxiMACiJIKFlDEYAFEaQ0BSDEQBVECT8CoMR9IrTNMiPIOG/GIwAqIsgQQgGIwASIEhGx2AEQBIEydAYjADIgyAZFIMRANkQJCNiMIIBcT0k+REkY2EwAiAtgmQgDEYAZEaQDIHBCID8ZA+S1WodPXp08/vtdnt5ebnnZr9+/bp27argurSEwQiAJkgdpOzs7O3bt1ut1uaf2r1798aNGzt27Oi+mZWVNWrUKGVXpwGkCICGSBqkurq6devWffLJJ507d27xAUVFRenp6ffdd5/CC9MQagRAW8xqL6BlmZmZ0dHRa9eube0BxcXFffv2tdvtDQ0NrT3G4iU8y5SUydRCjY4dK6BGAGQm6YS0cuVKs9l86NChFj/rdDrPnDmzZs0au91eV1c3Y8aMjIyM5g8rKSkJ8zJlxGAEQKMknZDMZl8Ls9lsSUlJW7Zsyc/Pz83NtVqt27dvV2xt0mIwAqBpkgbJt7i4uKysrLi4OCFETEzMhAkTCgqM/m8ugxHgG6dpkJ8mg1RRUbFz507PTYfDERERoeJ61MVgBEAftBSkEydOVFdXCyHq6+tXrVpVVlYmhLDZbAcOHJgyZYraq1MHgxEA3ZD0oIYWZWZmTp48OSUlxWKxpKenp6amDhw4sLCwcMmSJQb8IyRSBEBndHv6W4vFouOj7KgR0FaJiYlqLwFXoKUJCYIUAdAvLb2HBGoEBMzU2jmGIQ0mJG0gRQB0jyDJjitHADAIgiQ1BiMAxkGQJMVgBMBoCJKMGIwAGBBBkguDEQDDIkgSYTACYGQESQoMRgBAkNTHYAQAgiCpi8EIUIxez9upJwRJNQxGAOCNIKmAwQgAmiNISmMwAoAWESTlMBgBgA8ESSEMRgDgG0EKO1IEyMBk0u0FsnWDC/SFFzUCAD8xIYULKQKANmFCCgtqBABtxYQUYqQIAALDhBRK1AgAAsaEFBqkCACCxIQUAtQIAILHhBQUUgQAocKEFDhqBAAhxIQUCFIEaA6naZAfE1KbUSMACAcmpDYgRQAQPgTJL1w5AgDCjSBdGYMRACiAIPnCYAQAiiFIrWIwAvSE6yHJjyC1gMEIAJRHkJpiMAIAVRCk/2EwAgAVEaT/YjACAHURJAYjAJCC0YPEYAQAkjBukBiMAEAqBg0SgxEAyMZwQWIwAgA5GStIDEaAYXGaBvkZJUikCAAkZ4gL9FEjAJCf5oNktVp9fNZkaqFGx44VUCMAkI22g5Sdnf3UU0+19lkGIwDQEK2+h1RXV7du3bpPPvmkc+fOLT6gtLSkyT2kCABkptUJKTMzMzo6eu3ata09oF8/i/dNagQYnKm1v/mANLQ6Ia1cudJsNh86dMjHY44dKxg6NJEUAYAmaHVCMpv9Wjk1AgCt0GqQAAA6Q5AAAFLQbZBKS0vVXgIAoA10GyQAgLaY9HrCQZPJdOzYMbVXAUAWQ4cO1es/d7rBhAQAkAJBAgBIgSABMAT218mPIAEApECQAABSIEgAACkQJACAFHQbpH79+qm9BABAG+g2SADgjeshyY8gAQCkQJAAAFIgSAAAKRAkAIAUdBskrocEANqi2yABALSFIAEApECQAABSIEgAACkQJACGwPWQ5EeQAABSIEgAACkQJACAFAgSAEAKug0S10MCAG3RbZAAwBvXQ5IfQQIASIEgAQCkQJAAAFIgSAAAKeg2SFwPCQC0RbdBAgBoC0ECAEiBIAEApECQAABSIEgADIHrIcmPIAEApECQAABSIEgAACkQJACAFHQbJK6HBADaotsgAYA3rockP4IEAJACQQIASIEgAQCkQJAAAFLQbZC4HhIAaEs7tRfQqsrKypKSkl69elksluaftdvt5eXlnpv9+vXr2rWrgqsDAISYpEHat2/fCy+8cNtttxUUFEydOnXp0qVNHrB79+6NGzd27NjRfTMrK2vUqFGKLxMAEDIyBsnpdK5ateq9996Lj4+32+3jx4+fOnVq7969vR9TVFSUnp5+3333qbRGAECIyfge0ueffx4VFRUfHy+EiI6OHjNmzOHDh5s8pri4uG/fvna7vaGhQY01AgBCTMYJqa6urn///p6bXbp0aXKEgtPpPHPmzJo1a+x2e11d3YwZMzIyMhRfJgAt4XpI8pNxQnI6nWbz/xZmNptdLpf3A2w2W1JS0pYtW/Lz83Nzc61W6/bt2xVfJgAglGQMUseOHZ1Op+emy+Vq1+5Xk1xcXFxWVlZcXJwQIiYmZsKECQUFBUqvEgAQUjIG6brrrvv22289N2traxMTE70fUFFRsXPnTs9Nh8MRERGh3PoAAGEgY5CGDRsmhDh06JAQ4tSpU/n5+SNGjBBCnDhxorq6WghRX1+/atWqsrIyIYTNZjtw4MCUKVNUXTIAIFgyHtRgNpvXr1+/fPny+Pj4oqKidevWXXvttUKIzMzMyZMnp6SkWCyW9PT01NTUgQMHFhYWLlmypPkfIXE9JADQFpNejzyxWCzbtm1TexUAZDF06FC9/nOnGzLusgMAGBBBAgBIgSABAKRAkAAAUtBtkLgeEgBoi26DBADQFhn/Dgnwx1XPh/6voS8+uS/kzwnATwQJ8gpHcoL5juQKCCuCBFkon5+2anGFVAoIFYIEdcifHz813xASJSdO0yA/ggTlhDZC/XaeDeGzuZWmxAX/JCQKCIxuz2VnMpmOHTum9iqMLsgChSM5wQhJrgR9UkmTq9hAQgQJIRZwhGTLj5+CrxR9UgZBkh9BQmgE0CGNFuiKgkkUcQofgiQ/3b6HxPWQFNDWCOm1QE0030z/E+X9IyVOMBrdBgnh06YO6SlCFRUV77//flVVVVJS0sSJE/3/wiY/BB99suyqLvl/se6PiVNomUy63SGkGwQJ/vK/Q3qKkEdtbe2uXbuWL1/e2Ng4cuTIysrK+fPnB/ZU3j+fJnHy1KiJJj98+gRd0u3/MnDF2FDxs0O6jJC3PXv2PPzww+fPnxdCbNmyJScn58iRIyH/LgG8/0Sc/MQVY+XHhISWqdghm822adOmsrKy66+/fvbs2QkJCSH/FgFISkrKyclxf1xfX9+9e/dwfBcfw1NrPP+lKBO0jiDhV1Sfh4qLizds2PDcc8/Fxsbm5OQMHDjw1VdfXbRoUZi+nf+6dOmSnJwshHC5XJs2bdq6dWu4v2Nb48R7TtA63e6y47DvNlG9Qx533HHHm2++2bNnT/fNxYsXv/rqq4WFhZLMSUKIxx9//Lbbbps2bZpaC2jrbj3i5MYuO/kRJKPzJ0VKvj/Url27a665xv1WjRBiz54906dPz8jISE9PV2wNPuTk5MTHx48ePbqysrJXr15qL4c4tQFBkh+77AxKtg55zJs3z2xuet1Il8ul5Bpyc3N//PHHO++8s2vXrl9//XV5eXlSUlLXrl0//fTTm266afjw4Y2NjR988MHChQuVXFWL2K0HPSFIxiJthzyavDdTUFAghLj77ruV+e4ul+vxxx+fNWtW9+7dBw8evGzZspiYmAsXLgwePHjXrl3JyckNDQ3uRy5btkyZJfmPOEHr2GVnFFdMkYTHbV+4cKFv37733HPP66+/rsx3XL9+/axZs9z74vr06XPXXXdlZ2cnJyfX1NSE4yBvZbBbz41ddvJjQtI5LXbIIy0tbeTIkZs3bw7mSVwu1+XLl30/pkuXLu4Pevbs6a5RY2NjZWWlezLbs2dP872IGuL5T9zW48iFvuJEjeTHhKRP8u+au6Lnn3++vLw8+KOrjx49mp2d7fsxmZmZ11xzjfc9H3/8cXJy8qVLlyIjI4NcgJwMODZxclX5MSHpjaZHIo+cnJz6+np3jVwuV3FxccCHfQ8fPnz48OFt/Sqr1XrLLbfotUaCN5wgJYKkE/rokNuHH35YU1Pz7LPPum9+9913RUVFVwySy+VqbGzs0KFDMN/aarUOGzYsMjLy4MGDt956q/vOsrKy48ePz5w5M5hnllkwcRL0CaFDkDRPKymqra199tlny8rKamtrk5KSnnnmmfr6+qeeeqqqqurixYsLFixw/4t/5MiRRx99dOLEiYsXL3a5XA0NDWVlZStXrvTxzEePHl2xYoXZbI6Lizt+/PigQYM2btwYExPT1hV+/PHHd911165duxITEwsKChYsWOC+Pzs7e+3atYFtteYEc+4iQZwQHN0GSffXQ9JKh9zOnz9/7733vvzyywkJCfX19TfffHNNTU1VVdXq1av79+8/f/781NTUqqqqnj173nPPPT/++OOpU6e8v/yTTz5p7Zm3b9/+wAMPvP766w8++KAQorGxccKECUOGDPnqq6/a2qQePXokJiaazeZXXnll7969zz//fLdu3Y4ePTp37lwd77vzgThBYbo9qEGvZ/vW6NEKKSkpa9eu9fxfwuzZs9955x33+Rd27NiRmpoaERHxww8/tDUh33777ZAhQ0aPHn3gwAHPnd99992AAQPS0tKueCxDcw6Ho7Cw0P3ut8PhKCgoGD58uKYPsQsHjZ6SnMO+5afbCUl/tDUSefvmm2969OjhPbOePXtWCDF37lwhxNixY9PS0pKTkwPYybZixYqG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0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n assert(isempty(strfind(filetext, num2str(ii))), ... \r\n 'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51456,"title":"Compute an improper integral of a ratio of algebraic functions","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105.083px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5417px; transform-origin: 407px 52.5417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 7.91667px; transform-origin: 152.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.0833px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5417px; text-align: left; transform-origin: 384px 22.5417px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\" style=\"width: 193px; height: 45px;\" width=\"193\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.217px 7.91667px; transform-origin: 138.217px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive real numbers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = integRatioAlg(a,b)\r\n y = f(a,b);\r\nend","test_suite":"%%\r\na = 2;\r\nb = 1; \r\ny_correct = 0.523598775598299;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 1; \r\ny_correct = 0.392699081698724;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 5; \r\nb = 2; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 4;\r\nb = 5; \r\ny_correct = 0.174532925199433;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 7; \r\nb = 6; \r\ny_correct = 0.120830486676530;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 1; \r\nb = 6; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 9; \r\ny_correct = 0.092399783929112;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 3; \r\ny_correct = 0.142799666072263;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 11; \r\nb = 13; \r\ny_correct = 0.065449846949787;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 19; \r\nb = 17; \r\ny_correct = 0.043633231299858;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 23; \r\nb = 29; \r\ny_correct = 0.030207621669133;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 31; \r\nb = 37; \r\ny_correct = 0.023099945982278;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 41; \r\nb = 43; \r\ny_correct = 0.018699956271368;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 59; \r\nb = 53; \r\ny_correct = 0.014024967203526;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 61; \r\nb = 67; \r\ny_correct = 0.012271846303085;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 79; \r\nb = 71; \r\ny_correct = 0.010471975511966;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 83; \r\nb = 89; \r\ny_correct = 0.009132536783691;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 91; \r\nb = 97; \r\ny_correct = 0.008355299610611;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 50*rand;\r\nb = 0;\r\ny_correct = pi/(2*a);\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\nfiletext = fileread('integRatioAlg.m');\r\nillegalfns = contains(filetext, 'integral') || contains(filetext, 'quad'); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-17T03:39:24.000Z","updated_at":"2021-04-17T03:42:40.000Z","published_at":"2021-04-17T03:42:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\infty\\\\frac{x^2dx}{x^4+(a^2+b^2)x^2+a^2b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive real numbers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50504,"title":"Find the area between curves (P3)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 541px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 270.5px; transform-origin: 407px 270.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"87.5\" height=\"18\" style=\"width: 87.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.4208, 0.5101, 0.2569, 0.1252, 1.1838]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1; \r\nb = 0.5;\r\n\r\ny_correct = 0.4208;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nb = 0.5; \r\n\r\ny_correct = 0.5101;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(1); \r\nb = 1; \r\n\r\ny_correct = 0.2569;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0.5;\r\nb = 0.4;\r\n\r\ny_correct = 0.1252;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = sqrt(2);\r\nb = 0.1;\r\n\r\ny_correct = 1.1838;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T18:50:42.000Z","updated_at":"2026-02-05T14:11:12.000Z","published_at":"2021-02-19T18:51:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = sin(ax)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = bx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=1 , 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":685,"title":"Image Processing 2.1.1 Planck Integral","description":"Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\r\n\r\nPlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\r\n\r\nc1'=1.88365e23; % sec^-1 cm^-2 micron^3\r\n\r\nc2=1.43879e4; % micron K\r\n\r\nMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\r\n\r\nRadiance : L = Me/pi in units of ph sec^-1 m^-2\r\n\r\nInput: (3.0 5.0 250) : From 3um to 5um at 250K\r\n\r\nOutput: 4.9612 E+018 : units ph/sec/m^2/ster\r\n\r\nPerformance Rqmts: \r\n\r\nAccuracy: \u003c0.001% error\r\n\r\nTime: \u003c100 msec (using cputime function)\r\n\r\n\r\nCorollary problem will include spectral transmission and emissivity.\r\n\r\n\r\nIR Calibration Reference:\r\n\r\n\u003chttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003e","description_html":"\u003cp\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/p\u003e\u003cp\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/p\u003e\u003cp\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/p\u003e\u003cp\u003ec2=1.43879e4; % micron K\u003c/p\u003e\u003cp\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/p\u003e\u003cp\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/p\u003e\u003cp\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/p\u003e\u003cp\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/p\u003e\u003cp\u003ePerformance Rqmts:\u003c/p\u003e\u003cp\u003eAccuracy: \u0026lt;0.001% error\u003c/p\u003e\u003cp\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/p\u003e\u003cp\u003eCorollary problem will include spectral transmission and emissivity.\u003c/p\u003e\u003cp\u003eIR Calibration Reference:\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\"\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function Radiance = Calc_Radiance(Lo,Hi,T)\r\n% Lo wavelength um\r\n% Hi wavelength um\r\n% T Blackbody Temperature (K)\r\n\r\n Radiance = T;\r\nend","test_suite":"%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=250.0;\r\n% Radiance = 4.96124998 e18 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.96124998e18; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=300.0;\r\n% Radiance = 4.1826971 e19 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.1826971e19; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=8.0;\r\nhi=12.0;\r\nT=280.0;\r\n% Radiance = 1.37122128 e21 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 1.37122128e21; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\n\r\n% Add random to block answer writers\r\nlo=3.0+rand\r\nhi=5.0+rand\r\nT=250.0;\r\n% Radiance = To be calculated ph/m2/sec/ster\r\n\r\nc1p=1.88365e23; % sec^-1cm^-2micron^3\r\nc2=1.43879e4; % micron K\r\nsteps=1000;\r\n\r\nx=lo:(hi-lo)/steps:hi;\r\n\r\n% Planck Vectorized for Trapz\r\ny=1e8./(x.^4.*(exp(c2./(x.*T))-1));\r\n% Leading 1e8 is for numerical processing accuracy\r\n\r\nz=trapz(x,y);\r\nrad_correct=z*1e4*c1p/pi()/1e8 % 1e4 normalizes from cm-2 to m-2\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-14T04:31:21.000Z","updated_at":"2025-12-10T03:26:46.000Z","published_at":"2012-05-14T05:39:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec2=1.43879e4; % micron K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePerformance Rqmts:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAccuracy: \u0026lt;0.001% error\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCorollary problem will include spectral transmission and emissivity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIR Calibration Reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59676,"title":"Write a code to implement the improved Euler's method to integrate a simple function","description":"Euler's method approximates the solution to a differential equation as\r\n\r\nwhere . It's possible to improve on Euler's method by doing the following:\r\n\r\n\r\nThe challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's improved method to integrate over equally-spaced points ( equal intervals) between times and . You must implement the boundary condition . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 227.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 113.75px; transform-origin: 407.5px 113.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEuler's method approximates the solution to a differential equation as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"177\" height=\"18.5\" style=\"width: 177px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44.5\" height=\"18\" style=\"width: 44.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. It's possible to improve on Euler's method by doing the following:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"283.5\" height=\"34.5\" style=\"width: 283.5px; height: 34.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.9167px; text-align: left; transform-origin: 384.5px 31.9167px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's improved method to integrate over \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equally-spaced points (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equal intervals) between times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" style=\"width: 14px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. You must implement the boundary condition \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18.5\" style=\"width: 63px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,x] = EulerImprovedIntegration(t0,tf,N,x0,func)\r\n t = 0;\r\n x = 0;\r\nend","test_suite":"%%\r\nt0=0; tf=1.5; \r\nfunc = @(t,x) 2*x*t;\r\nf=func;\r\nN=50;\r\nt = linspace(t0,tf,N);\r\nh = (tf-t0)/(N-1);\r\nnum_steps = length(t) - 1;\r\nx = zeros(1,num_steps + 1);\r\nx(1) = 1;\r\nfor i = 1:num_steps\r\n xstar = x(i) + h*f(t(i),x(i));\r\n x(i+1) = x(i) + h/2*(f(t(i),x(i)) + f(t(i+1),xstar));\r\nend\r\n\r\nx0=1;\r\n[t2,x2] = EulerImprovedIntegration(t0,tf,N,x0,func)\r\n\r\nassert(isequal(x(1),x2(1)))\r\nn1 = length(x);\r\nn2 = length(x2);\r\nassert(isequal(x(n1),x2(n2)))\r\nassert(isequal(n1,n2))\r\n\r\n%%\r\nt0=0; tf=1.5; \r\nfunc = @(t,x) x+t;\r\nf=func;\r\nN=50;\r\nt = linspace(t0,tf,N);\r\nh = (tf-t0)/(N-1);\r\nnum_steps = length(t) - 1;\r\nx = zeros(1,num_steps + 1);\r\nx(1) = 1;\r\nfor i = 1:num_steps\r\n xstar = x(i) + h*f(t(i),x(i));\r\n x(i+1) = x(i) + h/2*(f(t(i),x(i)) + f(t(i+1),xstar));\r\nend\r\n\r\nx0=1;\r\n[t2,x2] = EulerImprovedIntegration(t0,tf,N,x0,func)\r\n\r\nassert(isequal(x(1),x2(1)))\r\nn1 = length(x);\r\nn2 = length(x2);\r\nassert(isequal(x(n1),x2(n2)))\r\nassert(isequal(n1,n2))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4078801,"edited_by":4078801,"edited_at":"2024-03-05T14:42:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2024-03-05T14:42:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-02-29T19:23:54.000Z","updated_at":"2026-03-31T11:25:40.000Z","published_at":"2024-02-29T19:23:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEuler's method approximates the solution to a differential equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t+\\\\Delta t) = x(t) + h \\\\cdot f(x, t )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = \\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. It's possible to improve on Euler's method by doing the following:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^* = x(t) + h \\\\cdot f(x,t)\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t+\\\\Delta t) = x(t) + \\\\frac{h}{2} \\\\cdot (f(x,t) + f(t+\\\\Delta t, x^* ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's improved method to integrate over \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equally-spaced points (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equal intervals) between times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_f\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You must implement the boundary condition \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(0)=x0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43290,"title":"Calculate numerical integration.","description":" x=0:0.01:1\r\n y=@(x)x.^2\r\n\r\nUsing given two inputs(x and y), conduct numerical integration in x.\r\n\r\n(hint: trapz)","description_html":"\u003cpre class=\"language-matlab\"\u003ex=0:0.01:1\r\ny=@(x)x.^2\r\n\u003c/pre\u003e\u003cp\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/p\u003e\u003cp\u003e(hint: trapz)\u003c/p\u003e","function_template":"function z = integralx2(x,y)\r\n z=\r\nend","test_suite":"%%\r\nx=0:0.01:1;\r\ny=@(x)x.^2\r\nz_correct = 0.3334\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n\r\n\r\n%%\r\nx=0:0.01:1;\r\ny=@(x)x.^3\r\nz_correct = 0.25\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-15T05:49:20.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-10T05:41:31.000Z","updated_at":"2025-11-29T14:58:18.000Z","published_at":"2016-10-10T05:41:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=0:0.01:1\\ny=@(x)x.^2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(hint: trapz)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAAAoCAYAAADXNiVcAAAG+0lEQVR4Xu2aBYilVRiGn7XFLmxFVOxO7E5UFLu7u8Uu7MIWxU4UO1CxsAsTE+zC7g6e5Ttyd/afmXPuf2dn9t57YNlh5vwnvvfL9zvD6I6OlcCwjr159+J0we9gJeiC3wW/gyXQwVfvWn4X/A6WQAdffbAt3/2XAD4BPmoBDjMC0wPPAP+2YL22XmIwwR8L2AX4BrihRWCNAWwOjA1cDfzV1ujVvFwrwHeNWYHlgSmB14BHgJ/7OJvA7wN82kLg03aeZ1NgvK4C9K0ddcEfHzgAWBrYD5gFuAc4Azgc+L2X7QVnGeCQfpSkWd32XCcCdwEPNbtIu39XB/wxgf0DdMF8LH4+E7gZ2BH4vkKAswNnAQcBbwyggOcATgH2Bd4fwH2GytILAKsAi8Nw8m5vYF7gKGAeYFvgzsbD1gF/0QD5YWDPsODJgXWBp4C3KqSiwhwN/AqcCvw9gJLzbnqjSYFjB3ivAbxG0dLLAY+G1zWBHgf4GLgPOL6nHJoFP4F4JLAlcG3mEdXAS4DdgFcyv6kzbX7gQmBn4PU6C40m324BnAZcB7wDXAasBdwObADc2grLN7ZfD2jpGxYAqSUuBOwB/DgKBDoRcD7wUoSadi7/tPKTw9tdEbnYt+EFxGiTnt64WctXi24Jd7IV8FUGkJMAlwIvAidlzG/VlMOAhfvIQVq1z2CvM1144KmBHSL0Jpn/AuwF/FDX8hs17ILQsN8ybq4LNhE8ELgjY36rppiDnABsDLzZqkWH4DpWXPcCFwNHRKU1J3BTuP/zeuY9uZZv6WSGLinT2+hPEVYFrgTWAV7IEN4EwGLA+sDqwFQ9MlZduhWDIeSB0OwvK9ZdJLLcbWJextZDYspkwFLARsAKgAZmTE+ymwY4LjgNY/tnAbou/v64gR5a0K3GfgI+AL5Ot8sFv1EaS8biCn+1AoFuHaXhSLGnF1HPEL//M5IYw4usnWD/E6FDpZQeliV0/Q8r1rLkuxGwBL2qEFaFfU3hN1XT5TSeKFzHkvg7QNdtkrxi3NkkWzJNLsWqSaN6LnKo2UIOlrbJQ1uVnQ3MFF7Bb4aPZsBXyFqwGqhGvZt5KQ+9UmivzF7J0ONcFHuqBHoPSxiTzv6SOAUifWzGa7lTMgYT/HROKyvPbe5yN7B7cBfex7LOMXNk+CqBxJnkWuJhlLteW+UfgXcpBb/xIH0ROVUC9hDGJQX6v+vJRCK57mlDe00wj8nk7qeIREjLKwU/83gDPs28RbBfBV4OQs3kuT/F7/NgpeCn7NG4InHiv9wD1AE/ZbLGPkklrd9OYM5oB/BTsmwoMHSNlLnnCKLnnFLwkwvVEnX5xtLcUcft26QxxunydGGHAn9kbpxivmcdlSVm5vGyppn8me+sHXmTMqg9SsFP9KHsUQm540FLE77Gy3lOM3u5eqnKXG7BNRL4Ml+5TGRtwbZ4gXGB04NGt5STLPs/cWt2r1LwU+L1YPTNq0qr3s5SWuo1rpP6CCY2pYpnnvF4tJxtPpWMoZDwed71wvKtsGyXe67SpHmke5eA3yy5kzZNFmiXqYTkkbE6J0rK7aP2LeknWFrqNUoqk3TmoQD+XBGu5OUNWxMCazZROtYCvzHu7BpZd4kVJZ797ei15ySKPvo4OFqyZrvGfb2PQjCHsN5fNjjrLyoOk6oTq4TUeSw582DPleiSr7eysjFl3F8DSPJXPtb/PlsbgbrNOXiJ5SeqcL4mXajnkXM2afF/mw49h+eZOGhIXwJtBkgqWbsa41LYSXHfLqFEk0xX1cMRyRAFpvBkwYb68BmaFZVsnuSWD2VUcGt0R6r3jfv+zXBgNSOLl2NMI9y/BHxjtrThkxHvpQpLh93Ay8Oan634eEHgtugW6iFk7Gz/Jqv2oYJ/15L1BFKWCqHK6l1+5fAQPmQYHR50aBgSVwL/Xli0ni89iUsNNTuiGsDnQf709WSuV4xKwDfDVAPrZJvphYmvbKueeRnfde2SGrJy5gdeMA3pXB+DWDl4eX/u7dWvGbIPRnxTWJsQKdXyJuebF9mCtu3t/1Yoja1v+xv+Tm+nESkrqe2mRi74jY2dkmSr6lApgbN0eb6pU+d9ZFkqLyAhUlKV5K3eBrNywU8Mm0pgHNYl1RmWXzZofME7EMCMKgWrI4NB/zYX/NQrtjvUivdw7mvWOnckK7298m1GQCqojzbNgKWCixOhZjYdHb+pAl8ixWdAPq7cLvrEAm7yJLMmydKK4d726eWtz20FYwUIvG7eZNKOVxf4PpCqAj910My0dfH2gSVZdNGphdgK8NMaPkqwjKt65l26j6WdiV5u06d0/baaXwW+xIF1+E7A04BEg+D7CLI72kgCuTG/ja7cvUqSQBf8DtaFLvhd8DtYAh189f8AQYWAOJHhcZoAAAAASUVORK5CYII=\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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\" 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src=\"data:image/png;base64,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\" width=\"32.5\" height=\"19\" style=\"width: 32.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\" and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1, 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43003,"title":"Simpsons's rule (but not Homer Simpson)","description":"I wonder what Homer Simpson would have thought of Simpson's rule? Somehow I doubt his thoughts would have included the phrase Newton-Cotes, or even numerical integration.\r\n\r\nIn this problem, I want you to use \u003chttps://en.wikipedia.org/wiki/Simpson%27s_rule Simpson's rule\u003e to integrate a function, provided as a list of points in a vector. The points must be equally spaced in x, so all that need be provided is the spacing between points in x. As well, I'll be nice and always give you an odd number of points, since that is important for Simpson's rule to work smoothly.\r\n\r\nAs a test case, we should know that the integral of cos(x) over the interval [0,pi/2] is 1, at least analytically that is true. Your Simpson's rule code, for only 7 points spanning that interval will do pretty well:\r\n\r\n deltax = pi/12;\r\n Fx = cos(linspace(0,pi/2,7));\r\n simpsInt(Fx,deltax)\r\n ans =\r\n 1.00002631217059\r\n\r\nThus, Fx is a vector of supplied function values, and deltax is the step size taken on the x-axis.\r\n\r\nHomer would be proud.","description_html":"\u003cp\u003eI wonder what Homer Simpson would have thought of Simpson's rule? Somehow I doubt his thoughts would have included the phrase Newton-Cotes, or even numerical integration.\u003c/p\u003e\u003cp\u003eIn this problem, I want you to use \u003ca href = \"https://en.wikipedia.org/wiki/Simpson%27s_rule\"\u003eSimpson's rule\u003c/a\u003e to integrate a function, provided as a list of points in a vector. The points must be equally spaced in x, so all that need be provided is the spacing between points in x. As well, I'll be nice and always give you an odd number of points, since that is important for Simpson's rule to work smoothly.\u003c/p\u003e\u003cp\u003eAs a test case, we should know that the integral of cos(x) over the interval [0,pi/2] is 1, at least analytically that is true. Your Simpson's rule code, for only 7 points spanning that interval will do pretty well:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edeltax = pi/12;\r\nFx = cos(linspace(0,pi/2,7));\r\nsimpsInt(Fx,deltax)\r\nans =\r\n 1.00002631217059\r\n\u003c/pre\u003e\u003cp\u003eThus, Fx is a vector of supplied function values, and deltax is the step size taken on the x-axis.\u003c/p\u003e\u003cp\u003eHomer would be proud.\u003c/p\u003e","function_template":"function y = simpsInt(Fx,deltax)\r\n % simple Simpson's rule integration.\r\n y = Fx;\r\nend\r\n","test_suite":"%%\r\ndeltax = pi/12;\r\nFx = cos(linspace(0,pi/2,7));\r\ny_correct = 1.00002631217059;\r\ntol = 1e-14;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 0.125;\r\nFx = exp((0:8)/8);\r\ny_correct = 1.7182841546999;\r\ntol = 1e-14;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = (0:10).^2;\r\ny_correct = 1000/3;\r\ntol = 1e-11;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = (0:10).^4;\r\ny_correct = 20001.3333333333333;\r\ntol = 1e-9;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = sin(-5:5);\r\ny_correct = 0;\r\ntol = 1e-15;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 0.25;\r\nFx = sin(0:.25:100);\r\ny_correct = 0.13768413796203;\r\ntol = 1e-15;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = double((0:10) \u003e= 5);\r\ny_correct = 5.66666666666667;\r\ntol = 1e-14;\r\nabs(simpsInt(Fx,deltax) - y_correct) \u003c tol\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":9,"created_by":544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":"2016-10-02T01:31:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-01T23:16:52.000Z","updated_at":"2026-04-04T10:41:35.000Z","published_at":"2016-10-01T23:16:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI wonder what Homer Simpson would have thought of Simpson's rule? Somehow I doubt his thoughts would have included the phrase Newton-Cotes, or even numerical integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, I want you to use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Simpson%27s_rule\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSimpson's rule\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e to integrate a function, provided as a list of points in a vector. The points must be equally spaced in x, so all that need be provided is the spacing between points in x. As well, I'll be nice and always give you an odd number of points, since that is important for Simpson's rule to work smoothly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs a test case, we should know that the integral of cos(x) over the interval [0,pi/2] is 1, at least analytically that is true. Your Simpson's rule code, for only 7 points spanning that interval will do pretty well:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[deltax = pi/12;\\nFx = cos(linspace(0,pi/2,7));\\nsimpsInt(Fx,deltax)\\nans =\\n 1.00002631217059]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThus, Fx is a vector of supplied function values, and deltax is the step size taken on the x-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHomer would be proud.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1031,"title":"Composite Trapezoidal Rule for Numeric Integration","description":"Use the trapezoidal rule to numerically integrate a function, _f(x)_, passed as the first argument, between upper and lower limits of integration, _x=a_ and _x=b_,passed as the second and third arguments, respectively. Use _n_ equal intervals, the optional fourth argument, for composite trapezoidal rule.","description_html":"\u003cp\u003eUse the trapezoidal rule to numerically integrate a function, \u003ci\u003ef(x)\u003c/i\u003e, passed as the first argument, between upper and lower limits of integration, \u003ci\u003ex=a\u003c/i\u003e and \u003ci\u003ex=b\u003c/i\u003e,passed as the second and third arguments, respectively. Use \u003ci\u003en\u003c/i\u003e equal intervals, the optional fourth argument, for composite trapezoidal rule.\u003c/p\u003e","function_template":"function I = trapezoidal_rule(f,a,b,n)\r\n% trap: composite trapezoidal rule quadrature\r\n% I = trap(f,a,b,n):\r\n% composite trapezoidal rule\r\n% input:\r\n% f = name of vectorized function to be integrated\r\n% a, b = integration limits\r\n% n = number of segments (default = 100)\r\n% output:\r\n% I = integral estimate\r\n\r\nend","test_suite":"%% Simple Trapezoidal Rule\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nassert(isequal(trapezoidal_rule(f,a,b,1),5280))\r\n\r\n%% Composite Trapezoidal Rule for 2 intervals\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nassert(isequal(trapezoidal_rule(f,a,b,2),2634))\r\n\r\n%% Composite Trapezoidal Rule for 4 intervals\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nassert(isequal(trapezoidal_rule(f,a,b,4),1516.875))\r\n\r\n%% Exact analytical comparison\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nP=polyint(p);\r\nI_correct=polyval(P,b)-polyval(P,a);\r\nI=trapezoidal_rule(f,a,b);\r\nassert(abs(I-I_correct)\u003c1)\r\n\r\n%% Exact analytical comparison--higher tolerance\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nI = trapezoidal_rule(f,a,b,1000);\r\nP=polyint(p);\r\nI_correct=polyval(P,b)-polyval(P,a);\r\nassert(abs(trapezoidal_rule(f,a,b,1000)-I_correct)\u003c1e-1)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":279,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-11-13T19:14:48.000Z","updated_at":"2026-04-04T10:48:38.000Z","published_at":"2012-11-13T20:00:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the trapezoidal rule to numerically integrate a function,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, passed as the first argument, between upper and lower limits of integration,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,passed as the second and third arguments, respectively. Use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e equal intervals, the optional fourth argument, for composite trapezoidal rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47874,"title":"Compute an integral of an exponential function","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 125px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 62.5px; transform-origin: 407px 62.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 7.91667px; transform-origin: 72.3583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem builds on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47673-area-under-standard-normal-curve\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 47673\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 225.583px 7.91667px; transform-origin: 225.583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which Mehmet OZC asks us to compute the area under the standard normal curve. Write a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 131px; height: 44px;\" width=\"131\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.8083px 7.91667px; transform-origin: 53.8083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = IntegralExpFn(a,b,p)\r\n y = f(a,b,p);\r\nend","test_suite":"%%\r\na = log(2); b = 1; p = 1;\r\ny_correct = 1/2;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = Inf; b = 1; p = 1;\r\ny_correct = 1;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = Inf; b = 1; p = 2;\r\ny_correct = sqrt(pi)/2;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = 3; b = 1; p = 3;\r\ny_correct = 0.8929795115691813;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = 1; b = 1/2; p = 1.5;\r\ny_correct = 0.8278055502117507;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = Inf; b = randi(10); p = 1/2;\r\ny_correct = 2/b^2;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = 0; b = 4; p = 7/2;\r\ny_correct = 0;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\nfiletext = fileread('IntegralExpFn.m');\r\nillegalfns = ~isempty(strfind(filetext, 'integral')) || ~isempty(strfind(filetext, 'quad')); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-10T04:36:31.000Z","updated_at":"2026-01-09T17:40:58.000Z","published_at":"2020-12-10T05:15:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem builds on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47673-area-under-standard-normal-curve\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 47673\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in which Mehmet OZC asks us to compute the area under the standard normal curve. Write a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\int_0^a \\\\exp(-b x^p) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50509,"title":"Find the area between curves (P4)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 601px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 300.5px; transform-origin: 407px 300.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"66\" height=\"19\" style=\"width: 66px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"67\" height=\"18\" style=\"width: 67px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Plot of curves for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"18\" style=\"width: 126px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b, c)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [6.5065, 6.3475, 0.1134, 9.4710, 4.0104]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1;\r\nb = 1;\r\nc = -2;\r\n\r\ny_correct = 6.5065;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1;\r\nb = 2.5;\r\nc = -5; \r\n\r\ny_correct = 6.3475;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0;\r\nb = 4.8;\r\nc = -0.5; \r\n\r\ny_correct = 0.1134;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = pi;\r\nc = -pi;\r\n\r\ny_correct = 9.4710;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2;\r\nb = 70;\r\nc = -6;\r\n\r\ny_correct = 4.0104;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-20T22:13:12.000Z","updated_at":"2026-01-18T15:37:37.000Z","published_at":"2021-02-20T22:13:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = y^4 - a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58394,"title":"Integrate a product of gamma functions","description":"Write a function to compute the following integral:\r\n\r\nwhere and is the gamma function, the subject of Cody Problem 46025.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.05px; transform-origin: 407px 52.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 8px; transform-origin: 152.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 196.5px; height: 44px;\" width=\"196.5\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.55px; text-align: left; transform-origin: 384px 10.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 20px;\" width=\"56\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.842px 8px; transform-origin: 117.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gamma function, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46025\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46025\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intGammaProduct(a)\r\n f = @(x) gamma(1+i*a*x)*gamma(1-i*a*x);\r\n y = trapz(x,f);\r\nend","test_suite":"%%\r\na = tan(1);\r\nI_correct = 1.008596722571773;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(2);\r\nI_correct = 1.110720734539592;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = log(3);\r\nI_correct = 1.429800433690064;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(4);\r\nI_correct = 0.028770138289325;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sinh(5);\r\nI_correct = 0.021168845856719;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = asinh(6);\r\nI_correct = 0.630391294450658;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-06-03T19:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-03T14:18:04.000Z","updated_at":"2026-01-26T04:29:04.000Z","published_at":"2023-06-03T14:18:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_{-\\\\infty}^\\\\infty \\\\Gamma(1+iax)\\\\Gamma(1-iax) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = \\\\sqrt{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gamma function, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46025\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46025\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51137,"title":"Compute an integral of a product of sinusoids","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.8px 7.91667px; transform-origin: 150.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\" style=\"width: 139px; height: 44px;\" width=\"139\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.91667px; transform-origin: 96.5917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are integers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1917px 7.91667px; transform-origin: 99.1917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but other functions are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intSinmCosn(m,n)\r\n y = f(m,n);\r\nend","test_suite":"%%\r\nm = 1;\r\nn = 0;\r\ny_correct = 2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 2;\r\ny_correct = pi/2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 2;\r\ny_correct = 2/3;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ny_correct = pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 2;\r\ny_correct = 4/15;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 4;\r\ny_correct = 3*pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 4;\r\ny_correct = 2/5;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 4;\r\ny_correct = pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 4;\r\ny_correct = 4/35;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 4;\r\ny_correct = 3*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 4;\r\ny_correct = 16/315;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 4;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 4;\r\ny_correct = 32/1155;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 6;\r\ny_correct = 5*pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 6;\r\ny_correct = 2/7;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 6;\r\ny_correct = 5*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 6;\r\ny_correct = 4/63;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 6;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 6;\r\ny_correct = 16/693;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 6;\r\ny_correct = 5*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 6;\r\ny_correct = 32/3003;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 8;\r\ny_correct = 35*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 8;\r\ny_correct = 2/9;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 8;\r\ny_correct = 7*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 8;\r\ny_correct = 4/99;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 8;\r\ny_correct = 7*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 8;\r\ny_correct = 16/1287;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 8;\r\ny_correct = 5*pi/2048;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 8;\r\ny_correct = 32/6435;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2*randi(9);\r\nn = m+1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 22;\r\ny_correct = 2/23;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 28;\r\ny_correct = 2/29;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('intSinmCosn.m');\r\nillegalfns = ~isempty(strfind(filetext, 'integral')) || ~isempty(strfind(filetext, 'quad')); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-23T00:29:43.000Z","updated_at":"2026-02-22T14:27:23.000Z","published_at":"2021-03-23T00:33:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\pi \\\\sin^mx\\\\cos^nxdx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are integers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e but other functions are allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58997,"title":"Compute the water table elevation in an unconfined aquifer with recharge","description":"Problem statement\r\nWrite a function to compute the water table elevation above the bottom of the aquifer and the position of a groundwater divide given the water table elevations at , at , hydraulic conductivity , and recharge rate . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\r\n\r\nwhere is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position is \r\n\r\nwhere is the (unknown) flow at . Using Darcy’s law to replace provides a differential equation that can be integrated using the water table elevations at the boundaries to determine and a constant of integration.\r\nUnlike the flows in Cody Problem 58966, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.25px; transform-origin: 407px 419.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.792px 8px; transform-origin: 164.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the water table elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 8px; transform-origin: 101.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the water table elevations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.0667px 8px; transform-origin: 61.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and recharge rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" alt=\"i0\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.6px 8px; transform-origin: 27.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6583px 8px; transform-origin: 53.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in other \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91.5\" height=\"35\" alt=\"Q = -K(dh/dx)hw\" style=\"width: 91.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.967px 8px; transform-origin: 333.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" alt=\"Q = Q0 + i0 w x\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the (unknown) flow at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law to replace \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.633px 8px; transform-origin: 135.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAoCAYAAACSN4jeAAAC30lEQVRYR+1XTUhVQRTWvW1qZZsWtTDUbBNJ7VwoiCIkVNCysFq2MDJciIiCLsSVP9i+BImoTRkuhMJq0SaojaAgtUoI2tf3wRw4d+7MvWce78kD78DHfe/dmTnf+c6Zc+a1tjTpaG1SXi0VsdTIVIqdeMVuQYEbwCWgQ6nxDp9fAiupCvnzU3OMhBaBdmADeAaQDEc/sOSI/sDzOnBUK0ErsdMwsAzcBP4C94AXAaOcdwC0ASR3sZHEaOyDU4J2bkdICYdVfBhzX57iOVcLOYtiu9j4qtt8Dc/7JYYY0rduzi88zzaCmPaeRroMeaOJkdMFYC+VXJFivoGyEIrtWtdluBcR0yG0qsXNHwA8KDKsDpmI+V4vYNVjYzh0+LnkjCH8ua1jirEUsDTISMmT71gkRTdFaZNiPzGLRZQjpViytPxWFlh8B4xKlxLzN7eUCNm0LvnFzUKh9PPrIeZZe58O4yesG/Ty6wq+zwD7QA/ALsH9c63LQsx6qsrKhLzXB4mFuBvI1ccQMT+UVmK6vLDBs+Hrwbw9BZxTClHBz0AuXWKnUie/JZQT2HzWsQiFkCSfA6HG/s+ty3CJEZvH5HG3IOS9VkK85m80PAT4LUj2Cx0kUToTmRgxhvMbICUjViSZN5sArzl0IJjI+F2MFxHLFPGilkQlXjlyLJQjwBcn1XkXOhZhvnsEhO5noqyFWIZ02bWHyj0BhgF9heZl8SPAazSVKrup1p2YeCw5Yj2hXEdVJddYFhj2olAmKUYD0jfZXiZVOIV06MlTOAXIQahb8ovHb7wQCgnm1WvgK7CllKEqdwFW/FFA/1GhaiwlvZ4nUi4yByyWY/R4HTgE/riN5HpdpBTf0fgdRVbmS23UNqXU5Jp9rPLzXv8+EDYS7gPY5zoBlgkO1q8dYBuInc5YS7qGNZd9R8pOZZk6qe9Jbhpg85bBf1K5/wTHTczsSEXMLJWbWClWKZaqQOr8/+6UrClQAbvIAAAAAElFTkSuQmCC\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a constant of integration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.35px 8px; transform-origin: 58.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike the flows in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.383px 8px; transform-origin: 233.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 403.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 201.85px; text-align: left; transform-origin: 384px 201.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"586\" height=\"398\" style=\"vertical-align: baseline;width: 586px;height: 398px\" 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\" alt=\"Unconfined aquifer with recharge\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0)\r\n h = (h0+hL)/2;\r\n xd = x;\r\nend","test_suite":"%%\r\nL = 10; % Length (m) \r\nx = L/2; % Position where WTE is desired (m)\r\nh0 = 19.11; % Water table elevation at x = 0 (m)\r\nhL = 19.11; % Water table elevation at x = L (m)\r\nK = 5e-7; % Hydraulic conductivity (m/s)\r\ni0 = 6.9e-8; % Recharge rate (m/s)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = 19.2;\r\nxd_correct = 5;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1200; % Length (m) \r\nx = 0:300:1200; % Positions where WTE is desired (m)\r\nh0 = 25; % Water table elevation at x = 0 (m)\r\nhL = 23; % Water table elevation at x = L (m)\r\nK = 4; % Hydraulic conductivity (m/d)\r\ni0 = 2e-4; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 24.789 24.393 23.801 23.000];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 1200; % Length (m) \r\nx = 0:300:1200; % Positions where WTE is desired (m)\r\nh0 = 25; % Water table elevation at x = 0 (m)\r\nhL = 23; % Water table elevation at x = L (m)\r\nK = 4; % Hydraulic conductivity (m/d)\r\ni0 = 8e-4; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 25.593 25.475 24.637 23.000];\r\nxd_correct = 400;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500; % Length (m) \r\nx = [100 200 300 700 1200 1800 2400]; % Positions where WTE is desired (m)\r\nh0 = 35; % Water table elevation at x = 0 (m)\r\nhL = 33.5; % Water table elevation at x = L (m)\r\nK = 50; % Hydraulic conductivity (m/d)\r\ni0 = 1e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [35.010 35.014 35.012 34.949 34.74 34.296 33.633];\r\nxd_correct = 222.5;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500; % Length (m) \r\nx = [100 200 300 700 1200 1800 2400]; % Positions where WTE is desired (m)\r\nh0 = 35; % Water table elevation at x = 0 (m)\r\nhL = 33.5; % Water table elevation at x = L (m)\r\nK = 60; % Hydraulic conductivity (m/d)\r\ni0 = 1e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [34.998 34.992 34.981 34.889 34.665 34.235 33.621];\r\nxd_correct = 17;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 20; % Length (m) \r\nx = 0:4:20; % Positions where WTE is desired (m)\r\nh0 = 5; % Water table elevation at x = 0 (m)\r\nhL = 3.5; % Water table elevation at x = L (m)\r\nK = 0.5; % Hydraulic conductivity (m/d)\r\ni0 = 1e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 4.752 4.482 4.188 3.864 3.5];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 20; % Length (m) \r\nx = 0:4:20; % Positions where WTE is desired (m)\r\nh0 = 5; % Water table elevation at x = 0 (m)\r\nhL = 3.5; % Water table elevation at x = L (m)\r\nK = 0.1; % Hydraulic conductivity (m/d)\r\ni0 = 5e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 5.065 4.97 4.706 4.243 3.5];\r\nxd_correct = 3.625;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1000*rand; % Length (m) \r\nx = L/17; % Positions where WTE is desired (m)\r\nh0 = randi(100); % Water table elevation at x = 0 (m)\r\nhL = h0; % Water table elevation at x = L (m)\r\nK = 5; % Hydraulic conductivity (m/d)\r\ni0 = 5e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nassert(abs(xd-L/2)\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('unconfWithRecharge.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T01:49:39.000Z","updated_at":"2026-02-12T13:52:11.000Z","published_at":"2023-09-23T01:49:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the water table elevation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the water table elevations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and recharge rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in other \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Q0 + i0 w x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = Q_0 + i_0 w x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the (unknown) flow at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law to replace \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a constant of integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike the flows in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" 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Sequences 115: Integral involving square root, floor, and round functions","description":"Given a postive real number , we are asked to evaluate the following integral:\r\n \r\n where: the symbol \"\" is the floor function,\r\n and \"\" is the round (to the nearest integer) function.\r\nWe may rewrite the above function in Matlab as:\r\n\u003e\u003e S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\r\nTherefore, for , we have:\r\n\u003e\u003e s = S(10*pi)\r\ns =\r\n 12\r\nBe careful though, in using the Matlab integral function, as it is only an approximation. For example if :\r\n\u003e\u003e s = S(100000)\r\n\r\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\r\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\r\nrequested accuracy. \r\n\u003e In integralCalc/iterateScalarValued (line 372)\r\nIn integralCalc/vadapt (line 132)\r\nIn integralCalc (line 75)\r\nIn integral (line 87)\r\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \r\n\r\ns =\r\n 49841\r\nThe correct answer is . The integral function is off by only 2 units here, but the discrepancy could be even greater for other values of . integral function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 673px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 445.71875px 336.5px; transform-origin: 445.71875px 336.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-18px\"\u003e\u003cimg 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\" 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src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/round.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eround \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(to the nearest integer) function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe may rewrite the above function in Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 30px; transform-origin: 442.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; s = S(10*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBe careful though, in using the Matlab \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/integral.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efunction, as it is only an approximation. For example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"18\" style=\"width: 74px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 260px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 130px; transform-origin: 442.71875px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; s = S(100000)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eWarning: Reached the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003elimit on the maximum number of intervals in use. Approximate bound on error is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e8.0e+01. The integral \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003emay not exist\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e, or \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eit may be difficult to approximate numerically to the\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erequested \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eaccuracy. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt; In integralCalc/iterateScalarValued (line 372)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc/vadapt (line 132)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc (line 75)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegral (line 87)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e@(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 49841\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe correct answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"18\" style=\"width: 65px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n % NOTE: the following expression is inaccurate for some values of n\r\n s = round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n)); \r\nend","test_suite":"%%\r\nn = 1:20;\r\ns_correct = [0 0 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7 7];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:20).*pi;\r\ns_correct = [1 2 3 4 6 7 8 11 11 12 15 16 17 18 20 22 23 24 26 28];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100*exp(1);\r\ns_correct = 126;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 1234.5678;\r\ns_correct = 601;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 12345.6789;\r\ns_correct = 6125;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100000;\r\ns_correct = 49839;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 6e6;\r\ns_correct = 2998571;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 4e8*pi;\r\ns_correct = 628304194;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 10.^(1:10);\r\ns_correct = 5555500618;\r\nassert(isequal(sum(arrayfun(@S,n)),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:1e5).*exp(2);\r\ns = arrayfun(@S,n);\r\nss = round([sum(s) nnz(s) mean(s) median(s) mode(s) std(s) sum(num2str(s))]);\r\nss_correct = [18444149135 100000 184441 184439 303161 106553 37072130];\r\nassert(isequal(ss,ss_correct))\r\nassert(isempty(lastwarn))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-18T18:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-05-18T18:10:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-04T18:21:04.000Z","updated_at":"2023-05-18T18:10:26.000Z","published_at":"2023-05-05T19:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=S(n)=\\\\Bigg\\\\lfloor\\\\ \\\\int_0^n\\\\sqrt{\\\\lfloor{x}\\\\rfloor} - \\\\Big\\\\lfloor{\\\\sqrt{x} \\\\Big\\\\rfloor\\\\ \\\\mathrm{d}x\\\\ \\\\Bigg\\\\rceil \\\\cdot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e where: the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/round.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eround \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e(to the nearest integer) function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe may rewrite the above function in Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e s = S(10*pi)\\ns =\\n 12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBe careful though, in using the Matlab \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/integral.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003efunction, as it is only an approximation. For example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=100000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e s = S(100000)\\n\\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\\nrequested accuracy. \\n\u003e In integralCalc/iterateScalarValued (line 372)\\nIn integralCalc/vadapt (line 132)\\nIn integralCalc (line 75)\\nIn integral (line 87)\\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \\n\\ns =\\n 49841]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correct answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=49839\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59029,"title":"Compute the water table in a layered unconfined aquifer","description":"Write a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at and , and the length of the aquifer.\r\nBackground \r\nCody Problem 52070 dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \r\nFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE varies with , so does :\r\n\r\nThen using Darcy’s law as in Cody Problem 58966, one can write the flow through the aquifer as\r\n\r\nConservation of mass says that in steady one-dimensional flow, the flow past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions and to determine the flow and the constant of integration. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 836.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 418.15px; transform-origin: 407px 418.15px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.442px 8px; transform-origin: 367.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.775px 8px; transform-origin: 42.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 306.625px 8px; transform-origin: 306.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.125px 8px; transform-origin: 330.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321.408px 8px; transform-origin: 321.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.95px 8px; transform-origin: 36.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e varies with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.2167px 8px; transform-origin: 13.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, so does \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADEAAAAoCAYAAABXRRJPAAADqUlEQVRYR+2YS6hNURzG750ZUB4jEsKAokgeEQOFEiPlWboDeYxkQDGSAUIZKK8MDOSZZKIYmCmPCQMxQEwYecWc73fb3+1v3bPO3oezz7nprPo6e5+zHv/v/16nv+8/GP3/AYe+HomRYsWeJXqWaKMGytxptc7aIKwXJibn3tT7c+FY8f0Jfa4QFod5n/R8RTgufGmj3H9sVUbCkzfp4XpYeSgIHzeM8yDJvLd1Ce99/4YE2p3TQLML9d1DYXQhvC1UN4fKdeKGJNlYSIOG0XgcJvBDXw4ID2qXPBxQ1RIftcYxsUfP58Meu/V8TngibOuE+6QKqkJihha9CQtnFoKO1+c1geA/KdQavM0sW4XEQW1wtNjktT6XCRC7K4wR9ieW6aQnDZ5VhcT9QtvMvyi8L0hBaLvwrONSJwdWIUGwknEYZCZiAwLrhNrTZxUFlZEg6zzNbLRZ35O1uj7KSFCF8XkG2eeFsLN4xxqzu85AApSReKw5biOcgT4E90rTbVc4NSNBCv0cpFqjZ4pYtM5PvZOh2j0opguEd4JrEhmRgjtOuCAMxWMzErEPQtipgpu4WPyw0IE2siDOxgp3BIoo+98SSOn7hMPCLGFI9mYkYGv/xwJYwsNV2u8TAsF/4YOVcdF5xSa79EksXhauCrxz9vSouGYkorYbda0xXhr1U62SwX2Jt5fCkrDY7mt3HrZvjkTaaizSyrSo0W5QCD0azWmFiK2bKgxlMhp1zoM/5EhEd8m13qyP1sDsUYONCFB3dhQ/TNPnFmGVQBBz8cLX2YfaNEr4JdiliY0Y6EP750hE4SAxKaPSmKmYkku5bhanaM5egRhDwOiGvHPWcsGZx/s3TR4pCSwwIMQrJsJxKNnC6Y5584WtglsS80znQuCRMFlYKeCWtrRJuzNIrem+LRsPHFpW7DIGaOlrX6isTVL3JYH06dTsTpkGkwzkQd/GIFtl+7S6ScQEgYDk/2/CbSHe/kw09mNeW9re1E0i3vrWSvDcPx6vCneLGnexTa0zzA3qJuHAzN3LnbYd1DGBeG1pf1Y3idjK+1pLfTkinBZwI9eblKgzpNdlA7FuEhyMSxHUZDF6MNoHAttWsMbT+wnWKY0HDugEiawGix9Io3OFWB9swUrN5UggQRq9J8T/ski5tB+uK00V0Q0S1jJCfhWo4NzXzwpLBe4n9EtnhEr/InaDBBUczTPoWk8V8eHYIWa+C5XvKN0gURYjLf/eI9Gyympa8BvnzsspftiMbAAAAABJRU5ErkJggg==\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"172\" height=\"35\" alt=\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\" style=\"width: 172px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.8917px 8px; transform-origin: 90.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using Darcy’s law as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5083px 8px; transform-origin: 73.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one can write the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.0167px 8px; transform-origin: 70.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e through the aquifer as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"183\" height=\"35\" alt=\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\" style=\"width: 183px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.825px 8px; transform-origin: 224.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.058px 8px; transform-origin: 152.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"20\" alt=\"h(0) = h0\" style=\"width: 61px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64.5\" height=\"20\" alt=\"h(L) = hL\" style=\"width: 64.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.991667px 8px; transform-origin: 0.991667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to determine the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the constant of integration. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 346.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 173.35px; text-align: left; transform-origin: 384px 173.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"559\" height=\"341\" style=\"vertical-align: baseline;width: 559px;height: 341px\" 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22Pi5Ga3bpBX1I3uitVG2lZbN8pbviDjIVc/dQN/yJ9oJ5lPN0f7sn0ajz+8u/99b918u3/37l2Xj0snZ1e4731vP5GGYRgGYZP+FX/ym3Y/8He+6rpeiuSb9B/79j++++AXPG/35JOP779nzebz2c++Z/dt//j/2X3e7/9zez2+FvN1X/P7rivWHc3LXnEiDGdFs4MYvvZrv3b3xje+cffa1772pOd4+B3pwIbZDRwbYg42x9kvjufGGV02iLSdDG7KsWPjqQxdHG3vuecpHyvQZXOKD31X0MkWjEm7FcONcsbIc2zZ4LLZ5kC2r7aQOp0fzm3pr6S/bOvcsSWWcsW+bNFPu3deunf/23Uu7R7c/+NbfstO/gNcjp++59fu/wHum+75/Ktt/kPc/XHyD3GzzX+Q2/3DXI5hGIY7Bf8h5ws/5HmXP4lOv2nOf2j6b3z6L989/3nPubpBBzbonH/Ov/ZL95t4eP0P/9R1xbqT8ToMZ8u8SW94wQtesHvHO96xe/7zn797+9tP9/bS76S76TwEG9ytN+Jb5Kb+EMRBPzfUYN/Wm/ek6rqR7ezY6Npv/GNIO9g6N37WnPE8Tx026R1b8zgmxhZd/tpu5dRBLqmv79quxloef3jf5Nd4YL7KMwzD7QC/eeX7fvCNu7/yNb/7pOd0+CbdN+TAs23/FY54m/7Sz3z17o1vftvuxS/6oN1Pftdr5vkX7Gs1X3c5c+ZNeoG352zQgfZ63qbnW2w2p2ysaDsZVm/EOXjrzaa4k/UlnX9l7EC/6QO6N++J/kBd+lZvpsGNIXbHvL0X7FI3/eOPja24Sc48cgOMvmO0q42qOuabLWMJ/RkzdTvMQ53Mz+u9Iu1oqz7xzcdzqX20xHxau3vw6u/Mr78734O3/PlWn/Zf3PeFT3u776/azF+5Wd/s//yzfsH+jT7taX9d2jAMQ4XfkX691GcQG283375Nt/3ol75w37JRnw36cDOYN+kB30X/0A/90KubdDjt23T/4Wi+bWYzuwUb5i20R6+TieVGn83wVswaK/0l9Kdf0Pf1kPlkLONYK/uuNxab2ZUdm1k33G543Shv2XTjbra7DXz6PW1b43Txj829I+uTcvqsczoEttrokxZqbjle2z0nb/X9zv7qu/pP7O7bPed9P3t5pcwH5TA8k+EN7l/6m//7mb5JXz1XPvO3vnL33a/fzZv0FfOd9DOnf/X3DIXvoucGHc7ibTqbUjadbEY7mU1ObmIr6LmxrTK4keb8UMwaxzFz4ECG9Ju+2VBV/SpX9MEB+oCsFWSs07JlxyZU3NzW2Ak5+ra8Ql/6E/26adU++7daamJtVvHxlZv7LdIXoG8f2KbPFekr27TRP23NG+zrWg6+r8/bfL+zn9/T5/C7+m99zuc+/U1+vMGnrW/vPebt/TDcOfCWmzfp/CGi66F7k15Bh+NND794f/7iX/hBrR684c1v3f8BJDb+P/f2d5303vnMd9LPh3mTHvhd9Mpp3qbzJp2/Ovrk7vJmo+DmlU1oJ7OJdmO8JbMpcnNzDPg/Jk7FDXWHvlZs5Y9ca7ACnbQR+7dqcYzOeeIG9lBsN7Wdrj4cr3pp27Vs8rfYil3Zmk+OHTvvDvM5lLcQS11siWmb0Ac5bl/+th3a+5/8uSv9J+Tb+w943/930jsMw0XhrL6T/ps+91fs/ue/+KWXPzmevgF/y889uvsFn/qf7uVX/M5P3/2FP/7vPk2PPPxDSPzBo3f8wH+1u/vuKz8E+JWZO5X5Tvr58Ow/epkT+RkNv27x/vvv333mZ37m/vju7/7u3ate9ardr//1v373MR/zMbsP/uAP3r3whVe+j7bFIz//+O7x9z1rv0FkS2kLtCv5rsv/u/vup/6K2Zb8xPuuWLLJeOyxx3b3XO7D/tLlDQuyfuVQHDa/jNUj/XOecH7v5fF3Xx5/1t13XyMfMxdjYNfNQRn9tDEn+61FcowOcG1qvG6u18uzL9fiyY3YjqCz0n3OA/des4muetre/ey7du997+O7++69XKu7nn2131rgp2vR1Scb3pUerX47GCdPfKXcsZWTc+3iYFf7q61zqdBnvy12+zld3nxfuuv5u7vveWD38+9/aPfzz37R1eOJ+z9i947dS3bvuf+X7N59z8t2P3vXx+7e9cDH7x6591fsHrnrI3eP3P1Ldpee9UG7t93zCbsnnvWBu8d3H3DZ1wftjyfvum/3/rvuvSw/tLvn/Y/FFR+G4Sz58Tf93O4n/uXP7TfZp4U35H/sz/6dvfyjP/kzl///fbvP/JSP2p8LG9A//XXfvvvu7/sX+/P/7A9+3u6XvuxD97J8xX/+Tbs/8mf+zu6rv+zX757/4HN2P/Rj/2r35b/3s3cP3H/5c+gO36DD+97//t2zPuiTT86Gs2LepC+4667LH6nXURq/k355y3f1bTqbn3yTnG8Z69ve1RvJlBPsK7557uSVv5qH6L/zWd+GpwzH5A/dHJJ8gw41DtC3yitJvRXpB6oN8mouh9AX9rn5TlLnemJY65V/Nrv2IR+jV32u2mP8bq0F6eLVt+uHctryDzm/Y8h45KJ9bYVzqDrgX8Hlzf3+PN7e8+b+Sntp/xt0YL77Ogw9fif9u7//X+y+/r/+9056T4dv0uVVr/h1u6/8/Z+z/3WMbLDzDflHv+yFux/+tj9+zT1JDh/yyf/R7q98ze/Z/Vuf+4m7z//9/83+d7c/k96k75nvpJ85s0lfcKOb9NzgVdxE5savbixXcgcf/G4cunhJ9adt5lFZ+VzlA6v8kZ132uccUu6oOWcdQb+n1evqV22SHOvknF/OW3K8Qk654avk3KqfQ7bHkDXxvPOZesp1w9xdx5VutsZL3cyh83HaebPxXq2zYzjWvm7whTms6przR6Y99A9rP+B9b95detaVv5Q8X80Znil8w7f+0923/ZMfPvXXXdhc86sV/YujbM5f+7pv28vAXxV940+/bffwo1d+Oxp8zzf/J7tf9fEvOTk7+ZrH5Q04b+T5fer4+y2v/PO7b/mHP7j72e//L69u9O909nWYr7ucObNJX3Ajm3S+k85fHWXz5Oas20jk5vVGqb7cFBAr5Y5VHpn7yo86uUFdxTKOaGfczKPKK13gH74emltS5wldPObBD1z2VzrfSdYFtvKEjFv1ujHjr2zOC+JmPVYbTWCsbqS7jWqnk7qHdLr2UD3Mu/N9TC21P4aMcaxNR+a88sMYpN59u0f3fVu/NUfmt+YMtxtn9Z307/wbX7H/R6i/+ZWv2/+axYTf6PI93/Sf7D7sQ55/zR87qrBZ/Tf/wF/Yfe/rf3L/10s/5AXPPRm5s5lN+vkwm/QFN/omHXKTVjd5udHxAzw3odkH6Uu52ziCmzfGU95iK94hP9g6Z6g6+nYTxKZLf7DKreYEqeu4Gz58drWpeum308t5J51d+k750PxqrNU1XeXkXKlp/pebY6jzwFe2Z4Vxus0vY90mc9UP1V9ez84m316vWnxUPXwdY2trHseC79PYrOZ9WqxTV686lu3WP6zNzf1973v48vlTbxyH4WbBJv0Hf/Snd3/xj3/hSc9x+Cb9+17/45efp4/vfvWvfPn+HP7mt37f1T9cxBv1X/KyX7jfnEu3Sccf/LZ//7+/+iZ9NunDjTCb9AVnsUmXugHiQ7puziQ3a7nR60hbN2z1w7fDDd4qh2S1aUsfOa9VDs7fOVW/q5wOvX2G6htqbjWu550eMd0U1dhp53j6rnG2UDfp7FY+6d+Kw3hX08zTeTDfHLPNeULXdwxu+nLze72bTUh/6Yf+1bXLsdRZ9SedziEfx+obi74aF7JmqX9aaq1Oyyq/7FemPea35sh8NWe4EV79td+yu+/eu3d/9Mt+w0nP8bhRBzfh3blfZTn0X5nwl2/Snylfd9kz30k/c54hK+fmwiaGjR6tuJlik+OmiT4+dJXBMaBPP1WG1EXOD0o+kInFUWWotvjMw1jH+qA/c6iYs76PzambUyV9K6cvyDHY0iMmm5luLmnnePpOeStnQC+vqXYV9aqvro4pQ60pMG4s+vihktY+/YLzrD5rbTJ+h/raullc1ehQ7fTn/aM+/W5o7bPt0MbrbZt2tHWjna3j1Ufq2d/FzBiSsdMv0N+B7hbkcSOQQ0f2K9Pye+4fedZLr7b5++45+F33/N572h+779/d/6572/md98NpeN5zLz9X3vvEydnpYAPNBtxNOLARr+foHbNBx+b+++6++j32Z8oG3f+KMJwt8yZ9wfW+SX/bo+/dvePRa/+oApswNifKfmgfixsVNlEpAx/Ynb/V5kawX9nKMT62wD7nnvrpm02hOWzlpE2t56Ha1jxWeiuOse90lKEbsx7O65h6QtrbtwKdrKlybh47Mqcao+ZZx8nvtPWFarfqP0vY2Fa/XZ90Y1lfxq1t17LR3tLBR71G2Vb7VS6dbbar+VVqrv6gcLPo6g2133O+e9+9vX/iWQ9cPn/qTf587/7OgjfpbNT5h5+3mvomfb7uMtwI8yb9jHnXY09cfvhf2m9kPPiAEzZXWx+QfNjwQZsbH/1UGZ2VP3TyLW3KHGmLXGPCIR+Za/pQBmIA+kn6M3/stuqjD31ClXkrvJUH1BinmQekfadDnl7zQzmDtehySDpf2h57nZGpkW9noYunPbWpvtGrNupAxlvNyRaqnaz6j6W7l4B+wS86whibUWXGsnUscQPruLWtrWui9nkOxMm+2hrDmBX7D7VJN8+cb+Z6syFuR+33fPX2/m3P/rirb+1p+Wu1vLXn8I19fVM/3F488q5b/+8hfJucb9KH4UaYTfoZ89wH7mZrc3J2BT5A2MSwyXHjsQJdNiXAB2VucPjQTPC15U9f2Kcs5IRPfKxi+lWIzkfmCp2cOeoz7dkAeN7NJ204so4p57HKY3UNjp3Hyj51HMOnsv0132SVQ70enb226KQMqauctrKK5/WHrTq5gdO/8auOsalFxunqCvoT9dM25bxHzBffOcbGM/Vy84kNazLlbLuNah2veQjjlcxFP/bpJ9tVLFts6a96tf80NmBswU7SV6XrO08Oxcs5iJt6N/T5FZz9129OvnKTX7thE//E7qm1Pdx6eJN+q/GrLe+59MTuoQefWevjGfO9+5vMfN1lwY3+w1E2IWwQcsPiZoNzxyF1RZtEX51tyumnwocYH77aHBNzC/35wV/lLk+ofo29mltiHY6ZJ7mA/o+1Oa19zlcdbLp5Z3/1l3GNmRyyX5H5QWe/ilfpaoM/c0Z2k7dVy2QrTs15i2PrcRrI92b5Zc5uJFMWa5Kb6G7jyaY5r4Fk/6E27aDm0/mqNlUn55Z2jtH/1re9Y/fBH/T8dl4d1VfN4WbwvPf95P4rNs998o27u9/32NV/FDtfq7k58LvNeZP+mv/oN5303Fx4g84fM1q9Pf83Pv2X7/7+1/37J2d3JvN1l/NhNukLbuQ76Q8/+q7LH71X3qZ3H+7dJgVyE+JGhw8qP+iQV7ZJ9VNl3ixufQBmPCBm5tORGw7lzLWLqd9jNl41p470l/G7awBV3z64Hnv1c045b8ZTD1JXudaqux5S7bvrVvNLVvaH6q2v6tfzbKHqG4tNlfl1pG9BN/M7Zm0cQ+Z1jK9j9U/r9zQ4927DC7mxrpvsLbpNNK0b4M5XZ3NsvDqPtEu/h/wdq5v5d3M5a/yuPNz9/ndds5Gf32xz4/CddLhVm3Q49I+Y7/Qf1maTfj7Mf584Y/hO+pO7e/cbCTckHHwI0YJjbMb48EYGN0uA7AdHyp3tIT+CjE5+IPEBlbnRGs8xyBw6jA3KmdfWd8UZX81HX3zodj46f4n2Oc9D+tqkfMiePnXt45yaqc+8aNNvxkfWRrClP/u27DOefYJNrS11lYxTfdEm+nJeuf5qC6kP+qdlDP9dLO0yZ8Yzvy7XlQyrcdBXcox+vY9gdf+kr2PpdPHPphm/bko9F2RiocvmtcM8s3WjW1tJv1s2ne+uRd/8Ice6eUHny9hVFxiXHO90jyH9HcLvyHPw/fhjvlbjd+PnazWH4dcvctxK2IS7Ec82+4fhtMyb9AU3+ttd2EyAH0BsMIHNBh/YjvvhW/WP+eBI2y0/h3xqS25Vr/oF+pwHpJx6kPZ8qOHbPqh+gb4uLqRth/rOmQ9t693Z1vh1XlmPlX3G6uqcc0lZTnvNuxxr7C6O1LGt+OpCjZt1ZSOdse1PPcfAcfvBMdiyW5H2K6wXuXb6NZ+cc5LzFf3V2sCx8+w4tL5gdQ2J1V2bY/GehWPy2CI30VstG/LUXcWp+VQfUGPavyLnm/JFIP9qbL6N549IPXv33stX9pm7EbyR35M+nCHze9LPnNmkLzir76SDH4r54dx9UNYPdM7TzzEf6JB+qs8VKz0/5GoOHYdinBXmlB/m9cOXfn8wMq/O7tC8VvUwnnWDY+aPPnrZQmd7vTnqG9JHFyN1YaVvnkn1p60bosy1iy01h4y1ZbfK1f66PvSrbqdnzrXWnU1Hl3v6zjxrTTNmF7/W6XpY5ZKgUzen2aePboN8SMe65XgXq7Pt2rQ9jZ1tjQ25+a/XmRidTZI6x+ifJfVrNf7ayTv9r8FepF/B+Exlvu5yPswmfcF5fidd+NCtH8z5wVE/xGX1YV7tVxyKW+nyYF7d27vO9zG5Xm9Obl6UD4Guetolq3klx8ZDL+eRH/7M89h8K9Uu50SMrt5wbH2NeegarNCeN7h1M2RNah7WJPsybmdX51bjAHVJuYPx1IPuTXmSNjWvrmb6Xulm7MQYq9yvh8yl5npo7R+is6+b1rr5zfviLNoud+Oe1r7adT+cpc711i1rdN74j1wfevxHrvn98bfzd+O/8A/95d2/9Tm/YvcFv+FXnvQMN5vZpJ8Ps0lfcCNv0rc+JFabDOk+jLXlA2L1YS6rjcP1xE0yBzAP7WrMCnr48O02dLkmdXwrx6zvll7l0LyOJeNDzsl5JNmXut1ca46ruWYM+tGj3l18SNvKVh1W8bfA3+o6d+i3s2Osm9tWLsfkrE6uhe56VMxFbkQ3c8icYbVOnP9qPHFObCitnzC2lfshyPfYjWbqHmtnPQ5thrtNv9cU0s9ZtOmb2Hleud55H6N3FviVGn5LDTzviX+xby/6W/jf95/+1d2n/IoX717xOz/9pGe42cwm/XyYfzh6xvB70v3QpOWhTctD1g9Q4AHPByIHH5q8uasfmNUWubOp9rQZq5M7O8nYynygmwNgU+1WvtVjHl3MQzk5XnPq8jukl7Iffnyo0geZr3S2Va7XN+dkmwc4185Ov5DXP8/BeUD1j56y/cdec/U6anzzgvRT0abmcSi3tHOsm1tS8+hyXul4Dls2ym52u5qlPhBjNU/IHDJn6GR8y2o8cyUu6x3fGZ/xLp9DOC/A57GgSz7eg8pboGfu6nd2PFvV5dpwnvrp59g2N+b2S+ZBf57XFh+C3OlUiHez4B+4cvCPWzl+8r5/e3/kP2x9290f99Q/ar28MbsIvOfS47uHHnz63zAYbh7ze9LPh3mTvuAsv5MOfgD6oPYh74ec45ynLf3a0Md52lT7JGOt4kLGq3lL+tdW3Rp7ldNWrrA1nvl2aHNIL+niZK1hVY+KvmqdZesaQtrlHLocpfrgfHVNhDh1fR665iu/mSdUP+iiU3OpeUPXl9T6JTkGXR5Sc5ZVXFjZCLY1f85X9VCG1FvlkGvj0DpZjUvGWNUtdeo8quzmta73Q+B3NV8xv9wg27pxRWe1ic1aiPpbvrs2fbCZ7vTMYzW+0j8tW3O+VfAVGrj/yZ+7+o9Zb+bb93mTfuuZN+nnw/zoc8bwJh14CPMh5CE8XPMDtI6DH4L2Y2MfHwD5Fq6zF+2IlTJox6FvyNh8CGcsbDN+5sRYHRf7oevnQwcYW407ljnV/OCQXmeTZK1hVY+U01ets2xdQ0g7fTpuHWi7miQZI/VpgTjYqAfK9K/q0/mtuumHA10wh9V1hq4vc6/1Mwfk/K8oUPMAdbeunzrmKeqsrn/qJF0eW3p1XrSQa2NrncBqvOpB1hS6PKDTAWRrry5tN48q11w6yI9nJa2bWs8l5Yr6eT3pIw/a9Lm1kabFRj913JzU8XzVao+uNofaBB9Sx5IcW8my5ecY/PWS/mrJrbfv58G8SR/uVG7szhyW8BCuH04JH1Ld+OoD1T4e8HwwapP21RekL2UeyDUmGw42HuowxocvHwj6BftAXXKSHK92QF/nz77VONCf+sp1Piu9lIW+tIVj6pHyyr7rh5qDVDt9AzayZZ8xJGUx1mqOieMcq2udOtLpOqec30rWDujTd85HOeN7gGsDMgdlWOmYD6SN8uo+hMwj1+dKD/ApKUPqpVzXPuS4dHrgGrAFY+uHI9dKXTf24R9W80i55rLKT7xW10O1dV1mP32c27qhBs+BHHPcvGnF81VbfxCobfq3fwU6SeaRYytZtvzcCP5+eL46w+adw98L7++EdwN/I78P/v777tk9/Oi6TsNwuzKb9HPgrsuPpu7DiYc0H0IcyLIa7x6UPEz5UFx9+B3jCx9Vzz5t/OAW9YldwVb9Op52HpD9xAP7oIuX9inX+WQeK5skbc0l6wGdn5p3Zw/2c9S6VtIOlIm3qjF+uxhbNrA1R0nfgE3nUz3XGbJfq6m63fzg0Lzx2c1L3zUHyHqqlzZQdZyrfRkX0r7LGX18mM/qTX/q5Xy26pt+aTP3Or6qQ0K/G0LGa03F8YyJLOm/zqG7Vuqu5tE9+8T5Zfzs68YTYlXs68aEMWpV65ob6nrebbxrm3q0+LcG9kP2r9qtDf1pIC/Bb8eq/1jyjzut3r5zsHk/tIGfN+m3nvlO+vkwVT0H8i+Odh9MkB9oq3EelKsPHGz44OMDsMrQ+Uo6PX1A2qT/7kOQ1g+cBDttU99+Dh703RxW8VJOsIFurn6IdfbmAVkLMI8aT3+ZL3T2HH7IQuZXcxHj6psDnW5usIqBTXddEv1DVyfIeVWf2kDmZz41Z+N117rKHM6bja5xj81B9Jnzok2Mhy90taHtfII2mTOgL8jq1WO1LlI2X6h+gXF8QR2vORt3BWM1btYp7Ttf9mFj/Crj03rBah5dHsqQdlv1OQ9qXaX2c751/7luGWct5Ea9trA1ni0+9X09beXY+Z4V+fa9/uNV377zF1k5/FP88yb91nNR/hHxncZs0s+B7mHnB1jdAKhbx/3AAj9w0OVDSXhIMkZfylu+wA82xxzXB1SbHAM+DNSpumCMzA1qbRjjg0y9lFfx0he6xurmCtVXZ7+qVc09c7OlDzsPMCf16TdG0uWCzKaUOUv6lkMxqj6kTcqQcwXljF19pk2OmU/2ZTzttmTQR/pJGVY5SI5DrqXMCdB1Y2VbfXY25owuR11P2tS13627Gi/nlvrK+K196SPz3ZIrxq36OYfqAznj02Yu+GTeXgOObh7J6tppt6qPepljsuoHx+pz/EaoPl1jKWfLXN14Q54f0l/117b6oZ/8zLO2K3JsS+9G8e07333n+Bf3feHuTc/93bu3/PzzdrsP+fSrm3e+PuMGfhhuZ87vbnoG4wcR+IDjAc3hmK0PSMhxyQ8bP4ySHE9ZX933ZqHGEez9wEQ/oZ8PQXQ6v10MoM+8tuKKsrkQUxv60pek38xH0pc++JCSVV7QxbNPv1vzB/prDPOA1EWmP3XrOjomhnpbNimD87FO3dxok5yHpK4yGI++tFvJ0M2dVpDJV7nLMedEfdSDWgOo9pxv2WTO6DFOHHMH+wQ97v/VvQT65Ui/yvlfGCBj6Avol5XcxYWqn3NAZ3Uf5XWD9Jk5YlPnIdp4/XLcWOroK33X+dPX9Ut3vdSnPUSnu7UGtkDPjTTkBluf2a7GObe2tis/9hu32tWYGUPQE8ZuFu953/27h5/zqfvN+1uf87lXN/C8eecrNG7eb+S778Nws5lN+jnAh4kPaR5YfhD4AQUpix824gOfB51jjueHQepJ6ucHUZdL+oLMuevnfOUXMga1cKNHm3EhYyvnPIjJB4Q5qKMv/Ve/h/L3fGVvHFqOlR5kvYAPOPQ8IGVI/6B/20qNkTVexYCVTc6n2mSdVnODnEOV0TkUG/281it/q7k7DplXN55zksypzklZzHnLxrnkWOZun+S5OqBs/vr3eoExtnxCxs5r3l3/Lm5nU2GOqSc596xPYvy068BXPge0sTb47vzk/HO89ku9XsbratPJUOesT+pDnWodtLMV7LGV3EBvbaRri5652FY/XZv6tqeJQcuY0Hde/NRPv2X3wl/wC6/Gy5Y377t7Htpv3v3uO5t3N/B+fWbevt8Y853082Gqeg74kBY/CHhI8ZCG+nDvZMDX1ttwQeaBlH7EDwdyUN7yBX5wreai3PlOHR7eviU7zTwq+E5959rpZ/yt/LG/nrzUoRV8On/1/KBKv9qgT21E/37odWSMnIdkPFCn2jBuvJqXqAtpnzZQawTa0W7FrjlA5w+qL8h41sw4kPaQY7T6I36Xg7qZc/qw3uB4h7Gss7FoHVcna9Wtj8qhNeZBnz5SltTt4mKzWptbY/iDjId+5glb80j0d0ztnU/WPvs56j0DaZPXBIglKzl1zYs+5KyT88xYtOJ1MMe0t3Vsq60b8M7PoXFaODaGbYIfwUZSvl7w8cQTT5ycPZ2MDZxz+PUZ3sCzgfftO2/e8+07x7DNfCf9fJg/ZrTgev+Y0dsefe/u//u5R68+tHnAI/vgzg+K7kOooh0PIR4q9cOEh6QPVsjxjE1/zQH4YKgPMMaxTb+w1Q85J2NVMrZ08+g45BvMMetf65N1sa9jlVfqV1/A+JbvzgbSTuhb5ct5HXeMvjpvSBvH0wY/Ka9iCueHrl211aecxl/66mC8zh3sr/PrSN8rf9Llc5pY1Xf1d5r7Iqnxt3xkvqeNm3EO1UB/mW/GPWYemaP6GRcydtXNPCTH0gYyJ/uzNp2cm90tMn9kW/sqfgasOGZ8tZnOnOs8Op1j2fLlxv96qHP9LZ//a3Zf/Sf/9O5XfOInn/TcOBlDmfb+Sz++77v/Fv3hpovK/DGj82E26QtuZJP+jkcfPzl7iu6hKz48eWilfIitBzrgi7fEdTxj4KP7IATt1K/9Z0WdR+a0yr3LN+UEH3Wekv5r7Q/V13FY6UCtN6h/mvl0uXbzWeVdbXI855JUH5Uai3PzXsXP+lad9LflC7Zq1+VT6XzKVq2SrRySzj7n2mF96hy6mmRt9Zuou/IlxpOVbmcH1X+S+ULGcezQPCD9HKp/6uqv5gFdLh3po5OhxuzqdijG1vhpyZoeg/qrDfmhTXxtV5t64nRj2b+SE/rZpH/Fq/7k7td8+mccjHsekMPu8Yf38kOP/8h+8w7Ped/PXr6aT+7lO53ZpJ8P83WXc4AHsf+ZlLY+tHnI0SqzkebBzTkPFuUObXgo4LfzvX9gXAZf3cM+YzDOA009P0zSTn3o4tHW2FDHsy/18Jl+wXjVv7WSTsZXV/tuXP9Qa9/llfk7ro5jtCnXeidZW+jkjCHa5Tqj7daFrK4jaJN1U8e5dNe21hiMUWuR6xzMV+g3vqx80a5qt8qnzg/0l3nAqlYZH2oO3kvHxFIvSf851s2zy0M7jhpfOl/apMzR6UJnZy451uXgHO3PsUPzSF3YWgPq1njJKhf767pInU72POny89pxgC0wX8fUOy3akj81YoNe77UV6tPqI1s3wOpwnhvj2l/tbVf+6Ze0z/4KY3ffffe+3cr9etpjIB6/OpLD777n12fqd9/vxK/PzHfSz4ep6jnAgzgfFuBDEw59qCj7oMC22m99j9qYW2Q89e2zP+FDrH54QJ0Lvuo4/rA/lD8tZA7Vv2N5mJvn+DEXSf0cT/+gDlxv/QVZX7TWIGsBmb+yLeifNkGfObjOuvVWbfRLf9WhtS7g/MF+bbIvISfn3NXCI2OtfG75EsZr/XJO+uDImN3cKl2tIOND5qCfY2Lpc+WfPjD/nCd0eTiW8ZPOlza53iX1lG3BvLVJnzUHdcH+ag+ZU/rodCFzS9ta92Oemat+6WqUfdo7bj6ZH+DbfvRtgc2toAfVd40jq7UGyI4bT/vqR+rGmxaw1Rf93YbcjfuqRY82/QK2suqvPPe5H/i076RnrJxD9te207tR8JW/OtINfP3u++3+j1fnO+nnw3zdZcGNfN3l4UffdflGu+/qAxnyIUh/PqAEHR7k2d89PPW7NZbo1wf+llxzSlbx6lxSr6sBfch8UGCT+qt8uhjq6g+25l/tq271aV/FMT40av6Mddc2qfpSc0o9awX0d3mubLfmlH471MU27SDjAeO1zqvrVvukziF1t+qqj8yzxqmkzYrM7VCtAP3OXxcrfSfoOFc2Cd21qzHoP2a+6GzdM/Z116jTg7yPt2qUNhlfzE25xk+qLnIXWztzr35gNa/sT9QxbjcXyHGouSRpX+2kiwGniZOoh71rLWvOGsxN8o2SG/e8TrnWr6fFF193edUf+VPXfN3lGLtK5rI1924ufh6cFfftHt3d/7637r/7Dhf9++/zdZfzYd6knwO5Qc8Hpgd9PFTz5ubhANkP6PPhw4NUe7HfFvCNL1plwK9sycROH0mXCzpdzh5J9tFqk/1dPlUG9HlAAjnow1rS5zygzo15rPQSfK7qX/PnwFfNtZL6SZ7jJ/Uyd8g86QfnA9rB1pzMU9/ai7qMZR226pc+PT+0xj2g001fxqOVtLfd0gfnQ/9KB1/H1gqMXdFP2tGX/j1n3A3CP/mub9/9ps//1btXf+Ur9v3oQebA8a1/+5t2X/S7fsvui37P79i989FHnjaODNREcv5CfOiukaBvrhzqpQx5L4L61iHnDZlbvXaHdGtsMaYg13onOU5s4zsH0M7nD6SdPjNHUKf6A31yOJ+t+l1vnEQ97PmvDL5BFua3ZX8szgPfNQa4KT5tqy/88yYdOGc8Y9lW+47UAXOvbfqVlM+Eex66+vY9f30kf3mVgzfw+TUa38TP74G/s5g36QvO6k06N7QPUR6sPkAq+SDuOHZ8hbkYfyVD+iLnzB+ZB/vqgYRtnWfXl9Txms8W1jfrkvnXXB1DnwcuY6l/PfWv+SeO1RpuyYdygKqTY9XvVi2xw9eWPXLVqeeyyh3UTx36unhS/dWY1bbOdaWv324Oh/JJm5VuJ6dt9oH96tj/lV/6+3Z/929/815+41t+ft/WNcsG/Ssu68Ev/eUft/vG//Uf7evAxquiX6n5KHd1rLbHkP63ro2+u3s/9WBLF9A/Zj6Ar9TXd40J1WfqS/pdoc6hHCF1c/x64nS63fOzA19dDtit2sRnLXjdcsPczb1DP+kP8k36MX4AHzWHbNmEr/QOxaj53Sp8Gw/1jfyzd++9fKXO+B+1vuwVJ8JwVsyb9HPADToPKx/CgNzduOjxAFTmIUab4G/1doRzxvNAF5+eo2P8lSzaQM2ffnV5EJkPBzKk71Xflo0ydPq0jpmTfcC589eP5Nwcs48j55R04xyZ/7HfU5dOJobUXMyh5pFjUP3WGiTabNmLOurlGlPOuZubdDqQc+cDUNk44HwzJqzmqv8tfaD/kE/6PSDlqisrubMDfTLPrNGDz3veicaV9er8zPnNb37T7lVf+cp9332XNxV/4S99/d43evjLuSHX62Jc6w7ai/raclQ/K/AN1ScYWx38HdLb0jUvYExWPq0HpD44fmhdVOizv96jsvJXc4TUzfHriWN91KN1Hsh1HOwDc7DP+q3aBDv6yNXNb33TLc6HtqJe1c836ceAjRvxzMGW+8EccsMujq1abDpSR1byWcA/ZM3vw+cbef5Ra30j/7a7P+6638jPd9LPh9mknwN3Xb41eJDx8OMh78OeNsmHnQ9SUGYMHfXYBHZjPozV40bnQYMufYCOeisZ9KHdVv7GEB5s+tPe8a4PctxWWTp9ciQfdckP/+ZvrYxpf+qk7MMx59Tp1zkrm/dqzPptyRxJzSUf4Ksx/aTfJOfSyVt5oZOQAx9e9Ne6uBaSQ7UDdDKe+WlrS592q7mil+tA/ap3jM/MRbmr1UrWD3iefZI1YvznfvZn9jLU63/p0qXdb/+Nn325vbIh4g36i170kXtZcm7pm/yrv1UdPdcW0k/WpJP1m6iTOXQ16fSg04Ws3Wo+Umtd9bJ2jlef5kebMtR6p44+uhzTD8dW/WiPiaP/1Eu6cXxAPtcFPeN2bf7QB/hyDNjE1msq6LhZJo+VnqD3Yz/6Q7sX/aKPfJqudaj9xqDf8dTLHNywA32+TT/UdqSOMYkhKUvmnvJZkRv5tz37467ZyB/6as2lZ73g8qqYv9J6nszXXRbc6O9J54HmQy4fbkA/D14eWlDHQdtEvRyjjxuXm776q/3GPDRe6fITffDwAufmg8gHIXLXl/IqT0j9WtetWlXfK+oct3xC5lOpY5nvSgbOu7lXvWQ1Rg5sUPOarq5vUvPKnAC5m7Ns1UVSRznnXGNCnR86Nddj6OJVVj6tqdT4KznJ+OA8qx6g++r/+Mt2X//X/vL+/F/81Luu6uH/lV/0Bbtv/7Zv3Z//sT/1X+9+5+/6osu9ly5rXPuP1itdbvTV8y438+fa6ecYMu96bfN8Ja/slTNHMLfOrurCaddFvY6V9KFdwnjNMcF/XWuQ80jSX9L5Tr1jxjNmp39a8HeMH/M4pEutPvljX7r7xr/9HbsPf9FH7PsyZ7ievHOtdzjO51purrO/tiu9bnMOWzkwtmW3GjtLiHOVxx/efeSLPvzkZDgrzv7HsuHy4+GpN+kr8uGBbv1pn34OHjT1TYtj9nEzdg+j7AdlYhFzNZ7+OXxYdugjdThP38g8ZPKtZtqt8jBPSH3zSqyTraRvbLKeXW3FGCudzAdovYZ1TF9bstS5c9Q5gfFW+ZMD/fqDY+tAqwx8iHjuvIxf5VVdUq9bB6AeGDNzcQzImVrnuBjnmg+QE7p4Vb/zCdhu1WolJxkfsrbmYU58OD/6yCP7MXANMPa1r/2qqxv03/cH/oPd7/n9f2AvP7m7d+nPOXa5dbl21yWvr35Wa6nWSvRrf9ajk1f2oFznuRW36tKedl2kPn05V3W0X9UjdSvdWpMu7lYcyLnQ71HHoI5Dt07VB/o61KVVJrdK57PmsIJaSc4h63SILn+vMT5rbpwDn2vcp6njxrtr1QP8Y0+rbW217dCfpJw1uVHSb4U45LHnnoeutMOZsq7+cN3kmyxabzofBPRx+HAFHgYseB9WtByr/vQH+qwYhwe34z68oI5zdPmu4oJ2nZw4luMpb+UJ6tQ6gHXyoZcYB/2sJzIbxuqPFlK/I/OB1DWm1JrCal0AviT9miN0/ekfzDGvLzraptyBfs5JX2CO9OcHCeeQeQoy4x5gm/4yH+uU196cc97K0I1LjQdb/rSlzfV16JpWe8nrkTEhc6KmD9x398nZbr9W0f2H3/Z3dv/dn//T+75P+dRfs/vDX/Wa/ZjzWvlDXq33lAFfXZ0gx9DP2nVyoq32ylmTKnd5pQ5Hrr+tuJDzSXk1Xn2JPutcOc/6Zz2OrT/t1rMs4+IzdQ/lIq5VyLHuucRY5yv7lGmrrtQcOp+QvqTmZUu/pL11qnbQzbHDudf7Ps9Ze6lTW8Zzo05LbHPQ3xboVfQn5nMaiH2Izm/amccTjz89x+HGmU36OXDXyZt0YZH7oMoHQ/bzMLCfRe8DJrEfqj+OTgbjcK7f9J3jeQ7pB46JmzfwsX1wKE/I3CBrhV0lY6U/ZY70l/NjI6A+6ItWmQ9IbVIXUr+rae2zHubFJqTmAKt41b9kXUH/VZbMu5I5py39ytqlXp2LMeqcHU+MWWOLfZDjNQ/nxJH5KEvnD1vQJ2Q++s4+qOOgTvpSzxpwsLYeu/TUH2ghxx/+5z949Te5fMiHfNjuL/21//lpdYXOn0eXHyiv6iT0o7O6p6os2ulbH5A16WTYqiHnq/vFWOqq1+mb99a8aZVrDcSc7VeHwzHoZPyC+UrGhPSZ1POai1hDa2G8ruaOdc/bbg6QcVfXBlIvqTnUvPAH9EvWRrr51D7tgPE67yTjoZfnHYznhj3PadngEr9u5GubEBcObe5zXilL5t6Nr8DOupkf/xVvOHuOvyrD0eSbdPHcB4PQz8Fi50GGnG9bAJl+byhtIP2tZEgbYqV/yHHw3IeD5+psxSVPH3SH+ioZo8sTGPeDRR9ZK+RVrM6nvrJNm+pLkM0Xm1VsoE9da2ofZDxgrPZBFy/7IXOUHM8acGzl3dHFB+2tozHpdy41Rndd1KEVc9eneJ4xza3mkR90GTvlzh9YD89F/fS9ZS/apey54CPfpPNh+OWv+Hf2/1CU3+TyN//Xf3RN7pC+9FfXPP2Z37F10g/UuLJ1Hbd8g/E7GbZqSAw3PhV0urgrfXxlbs4DMoeav5iXuZ2m/mAMz2v8GvNQzY2R/cIY/vBrPFDOXNQ1xmoOKXOgf6hWNT/7wRwYyz79MX/pYsAxvpyXfdLVTXJdgddi1RKn9uGD/ty4Z8s4937aSfrpWuxk5UOIlXQ6aV/z5Fc6DmfPbNLPgcs/p1+9qb3xWdQ+eHw4JCxyHgw+PPIhYb/okwcbujwQO9k46uvDWGB/6qSMbvVzKK4Ygz5sgQcO56mX8VLeytP/xMs56K/WDTJW9cl1oa8+cNIG0lc31/QLnX7Oy/5cF0nX59z1kfOgj6PLLe1glStk3vpIe+X8Lwjpmz79q29OkjFklVPGBdqaS15D+pTNUVv6u/qkLDkHa6GecWmViZV+TmvPHCr4yDfpX/7K37174xvfuJd5g/6LftGL9zI+bKtfWnMBY2V+KQPnXZ3ST/YnqQMZ11jY1jUBmbOydbF+xu3GK+nPuB70VdSv84acd1cbqDlJ1sRx+8xN2fz0bZ4Zv5L+IWNpX3Ogn8N80q/9zrGLia/VHFKGzocx1Fnll7VGNtf0h63U2hsn7fSZcxRzyBg1ryRjA+d+htTNtxt6+3hmuAHfgnH19Jnnh1qpY9TE2nQtcSo5H3Vl3qSfD9eu6OGGec59z94vVh8CwE3ODcm5Dx/lJB8M2PswoQXtAJ/cKPR1MlT9pD6AoJPxcdq44Fw4uJGZA3JXB1jFPpSn42A8a+Z5xb6a8wr9cHRzFcZr7NTPvO1frYtOBn3QZ4x8EGdunZ1knp28igvIxvYcsg9y3JzUST2hL3OBjLvKJa9F+jWOfczHDxjwwyjnSivYkU/VgZpDxpXT2OccQP38PenPetZTv+rsf//ubz+RrlD9Ett1gR/zy1j02Z8y+lmnBJ1uTrSizuo6otvNGd3VWhavGeR45qEMxs1+Wljpd3l5ADluPcdWdYMcT5/KdU1u3Ze0kjr6dO7S9Wc++oWu33j40dcxcnefQZcfR7cGsFutSfzLMXPhnOtX/Rk/87aemVfWYouaaz3HJ336tU61ZRy9zHe1IU89+/WTY4dabLtcslVXbvRN+sMPP3wiDcls0s8BFiuL14dQ3uS04BgLnhveh4o3f94w6oI+9LOSpeYAxuKhTh8Pok5Om/Rj28nQzQV7ztHL+aTfLo9VnhyQsZR5AFMn6XT0kzBmW/V5KEHG7si5ivppq8zR1QMO1ckciZn9SdpxSK6rlQxd3PSjX/usl/lVfcdpOzmvXfV9KBfofOa1S1Zz1R6qTt5/NYcutvNR59ActJP8Pel/5s//ld3zn//8vcw/HP3e7/nHexnSr/7InRiSY9LlbP+K09SNc+Mau8tDzLm7tpCx63iXk7HU7XRg5dOauIaAHNA7ZK8tLYfzSlIHutoy1vXDsTU3jnVd1Vi/q/6cD+g361P7Vrl3+dFa36xXzQfMgXtM8l7v5oLskWR8Zfziwzjm1dWik48Fv7a5Sc7zJGvtuC2xGafNcfzl2KE2bdNH/jCgvtzIm/Qnnnhi9wmf8AknZ0PyVIWHM8PFWh8GLGzI/u7hlXCzq8+hD/CGWj0c0Ochx8MudYBY+KKvkxNj46vG6HKAOhd9KJuX/V0ePCR9QNCnDPkwyVjI+NNmpaMfdWjhNPrVVpwfY4dqBrUeK5kDG/PJHLNftOGoMYF+qfJWXOTVnAC9vHagDWTeVSYWNl2NulwqjPMhIis9QT/nCpkTpE7OR9/HrEVA9qhzWNXnQz70w06kKz8g/I9ff+XXLsIX/97fuv+Lo/okx6yZMRiDrOkqnrI26ulTjHeobluxqwy0+Kl1cRyMnf3GypyO1en0jQuZT9L56WylmxfUuukr/UPNF6ot/Y5BXZvEJ3bmItoSwzpkP2CXOvbhq4sl2mS9aoy8b1c5QtoAvqSLmXHg0H2QuRijQ33oZH1n7GPJeZivLWP5bAXH3EA7rl33xj3Ps7/apo+Mu3q+Xw9f+7Vfu/8q32tf+9qTnkHmjxktuNE/ZgTc4CxeHkzcuN7w9nlT5M0lVWdFPgB4IHW6x+h0rHKH7E//kg+39APKp8mlw7jEWtUwY6x0OrZ8dnTzq7Xp+ukzhn053sm0h0Av49kHXa4pV33jdrnWPuqdD3xRH/CXte3qDF2MFeaX+a+un3qgfOxaxF7/ibnWuSXG3pqrqPdFv+d3XP196G98y8/vf/j5K3/pz+3+1B971b6PX8H4N/+X/+2qP/0cGwdWOXc5HVs355rXo4udVH1Im5W/VT/nqZPz63RSTvS7Apst20O13fKfuUnXB/RbC0gZDsXJOhqj1i1Bx/u92q1i5XjGyOu3Av2cU+r/kl/0gfv7Y5UndPNLuvheO+cIWZO8tvU6Z4zMu5MPzV3YLHdzTDLnzAdys53nqd/ZwVZs5/ryF33Avj0tL3jBC3bveMc79v+l8O1vf/tJ7wDzJv2M4Tvplz+29jI3C3hDspCzjwVPnzJwI1SdLbi5eVBys690HUfXmMTIh4hx6at5Jj5Msj/9K2/5QTYXyNjS5ZPjgA8O+rtaZYwtHXPOeWzppw0y1PmJ+hw8+ADfaWcM9TqZeNTANmtxI9duJUPGhZor1D7kfMMijHlkbVOuqE/d2JzWOaYMmX/1u9JDJkbG79ajoNthrjUu1Nhbc/VwzvkmnXP44lf+B7vP+XW/YS9/3/f8k91r/sQf2cuALWzFybXLkTmbq3PfWuP0Y3Oa9ZexU4bUNz5j3Ths9TuWOlmPqqPc5ZfzMq8k/WzVNnGcY7XeOGe8Qh9xDtUc2Rid/sqWPuOae9oIOoxxvyMzD+YOnT6YT8r5XDw2R30wRlzw/qiom7Whr17rmi8yNvhN26xJJwt+u9idjH1Xr0r673SphRvwfA67xjinv55ny/Vgo66OLdgC8c3bWl4PvD1ngw608zb9WmaTfg5cflzt27wZWcAsZPu8efNGBm6SqgN5E6cM2nh+aByMoV7GhczBPPTLPLI/basfbnh1rYF2kjaH8nHcXHiAZC4rtnSI5QOKOPju9I2Z+aVuzk9bxgWbfJClnmSMlM0xPzBqLqJc80Df/DLXLm9J33Ws0+8wNtcK0u4YH+SATjdH6Obb+U291VqEnHN3LTq5m1uSsZOVL+ec30knX2AN8P30B55zZXPD99O///JmXR/OrfLTP/Wm/RvHF7/w6W+7sPFeytq6gXJeXd3q+st7PvVAXfJMOfWpAVgPWujmlXaQNsrdde70rDv3GX11XsrVLmWujTWDzE3Udc1knPSHHeegDS3U3A49Z1dzAeW0JVb1kTmae3I99cq1ztHZg7J6guzm3LVhjWxBu7Q1X/Qyd3OErGWta/pLGXJ+jq18aVfj60M5oR8yDjCPbIXzXJf1PGGsbtzr5yNk3nXdHwvfRf8v/ov/4uTsCvX8mc7T77ThhuEGZAFzEyIDC5lF7k3pjedNmGiXOuBNDCmDN0ynC8atcurRZ+zU4QGQfplHRV1IP+oyj5UtGK9+wGU+kPnqL+uYshwaF/rMwzmnDRDTca8toJPz04b8tVXHuWzFkJTB/CDHsk7KnV/rtZLNJ8mY0uW+ksEYyTE+kpxblTlW/rT1oK/LJ0EP0JMtmQ+pY2Jnjo7lmjcv/XRv0rX5ur/+Lftz+LIv+Xf2308HfQh+/tbf/Gu7z/60j9mf8zvW3/pzP7vvJxdIG/xbW+cF6FffkjaO6582QZdDGTv1jOFYVxs59v7pro1jUn3X/FxnUO0EGZ1jc+zi6Y9z9FexIHPLmlffkvpVznjUy02ZqAMr/1D9wmoOnZ9qX2VrCbb0Q94fgk6tv3aArvrKq/txNe9jrnHad74yD8Yk5YxRdbq8KuqYL+f1ebTC8cwTPOfg7ftp4bvovkWXeZt+LbNJPwe4aVjU3ATIPmi4IcCbGLzZ8kbRTpS5EfCDP28MyBssdXM8b3BkclFHPTB2+sx8UnflF7DxjRTUOJ0tLXarfPSRNQBa8wNlfcLWuPF92EPOGZSNmePaOiaMd/nLVozVdSZWd+3SV/XLh07qdnKtU61NlVe5QycbLznGR43NBzFjmQMyrPxVH921cqzTy2tRr4sHHBPb/HOMvNM36LO+SUcHG/z8yk/+tN2XfOlX7sf4YHvVV77iam7JV/3hL9/94f/oD+51/ZrMB3/Ih+7bujaEnLh/wU1Lp5doQ36yqkPKzCXzyDj4zJon9Xp3Pjy6a0P/yndiHPLVX9pt+ag5ZuyKvnNM31s1OPY5CzmXlEHbGkMf+dxJtmKof2y9YJWjMhAP7Ad8moexQRtwjQA6qa+Mv8wTOD+UryinftpXX8bO+maN1NVvV8vTQL7e2+Zu7fz8BvISc8hcRT2fE6dh9dZ83qY/xWzSzwFuHBc1rTcFLQs6b2L18iYH+rlx9MWhLX4q3Dhpg643FKT/9MHNho43GhgvOa1fwU/G2LJdkflgv4qT9QJ9ar8ah2N8agfMiX7GV7bqK69qXWPUOWoHXSzBVtKv+tY+4+v7UG0k5bQ5JBOzi79lC11sxhxPGZAP+WBTaB7m5JggUzfGO7leS/NYxeY8N5GQ8YDxzA3qm/Rq8+o/8if2/3gU/H66c6Ll+N++9X/efz0G3fe978m9Lm/SybObS0Ku3fpJueL8VnOtcsaoudD67OzA1pqnTnd98tpwMEb8tKOvm5c2kHadj0qNjbxVR3MHfW/VAPCbc9Yv4CPJuaQMWz6c72ljoJf2yN09SCtp38luCKkpOUPeH6mftc85QOrnJtM8rXnmmLLUOBx1DcKh+gL9eQ76BMfQq+tCn+mfdgv84iP3KNi5TsG8wfj2mddp36S/4Q1v2H3Zl33Z7qu/+qv3B7zqVa/aveY1r9l9yZd8ye71r3/9vu+Zzvx2lwXX+9tdHrv05O5nH750zY1TYWHzQFj9K+rEG8wbIWGMh4I+OEcvb0puNP0bt8ZTH1/cgMpV97R+k7QVcu1s0T2UywrjdPWCOn6a3Fc+K+bf+dWX89PnafMWYx26btjpAzJ+HTdG1mZr7ai/JVe25p8ybK2RLieoPipdTugesx5EHzWPQ7EPkbn9oS/9vbu/+7e/eS/X316hHl9z+S2f/6uv/mfjv/aNf2/3az79M/a66HCvsoEhzy/9ot+538z/03/+U23OXpeUnUfmlXQ2nUy8fOZtrSlI+6wl447V/noOqWtf6iWOQ5d/zbUj84OUIfNIVnkir/KtdH7T1tzqte9iJ/roxuBQjI7OV9bqNHn+4l/03P39sfpMVbfaZd5bdLlC5gMZBzxf5S1beaBfa7Hi2DwPgZ/MVZlnCTWuc1G+3t/uAte757rTmTfp54BvCaT+9MwC52azBfrVSVj8HMf8BI6eLTcTN2b6T91EO8al0z3Gr7nRJmmLzLGyhVUu6T9l0TdkzSTH6T9N7t3YMdclMXbOD8yryxlqDjWWdHGNaQxImxwX/Osr5UrabMl57SHjA/2OpVxjWx9Y5QTpA2pdGdtaj8i11tqK/mse+ltdS9m61hzk9zm/7tfv35TzNZV8+5i85CUv3v/+9E//zM/d677z0Ueu5oMfZT7k773vvt2lyz54k15zhrwuysbLvFbXUpkx4ok1yrd1q7fD1a/n2DB/yJiinqQfZOpN3km3LtJOzB/SxpxShmqrX33TruqIn6q7ikWbVL/6MGdwLvqwT1Y+wPNjYyRdrQ+tpUN56gN8k75aU8ZIu8wnWa2LrXxBPen0qp/Mw7mmDDmvTocWjL/Ks7OBbr62KZMDvuo49sQbzp55k77gRt6k/6ufe4Rluz93MefiR7Zf8oZhsXtTKWtXsX/LpsaSzo4P1mPf8Hd+M8cuJzlkyzgPjZpH6iRdLOeffcrd/I7NPf1Dl1POj/Fj4ssq58whWdUKjomNjvmu/CSHfHbjyHxwdH6PyTFBHw7VuJPBc+w7X0C/+aoD1e8xtYIun4y/8msewCZEqo6gm3o5L65tvkk3h0quAeStvLU/dt108YTxVR0g55l+OjvlGk8f3VxWsbu5ZS4d+K12mad56cdzbXxbCZlLF7fmjdzdaxmr+jF+UvUzD8hx6foSx7MO1aarm9RY+sk36bUWKzljr3SB80PzhswHql0l/SivqPPuMLa6W3lK2tR8bA/NI/moFz33RDo98ya9Z96knzEP3Pfs/V8crTcG5zw4eQABix85bwxt8gGRN50+uGmqv2oj6BEj4ylDteNGPPT9R+j82s8B1bdjh2wdN5/E8awD1FiAj9V4Nz99Q9VfjQH93XXJefGQk1V86eJkDvVY1QoYX8XGjjwz3+on37CoDzU3bLbGyQOd6/FHm1jrQz4g548M5pNvf2os81VOWzFPqPaysgN0D/k1jzyHqiPdBp04HNjwJh14k854zVs9fde1g019a1ZtVtR8jKsM+JHqE/vTXHuo1wQfHM6LsdoHxma8ex5mLlXmwC59dHmC+qCNb4RFP1BjQdWlv+YL2pJLzTfvS0l9yDxA20S/+HHe1SeY5zFryTjamiugS0zo6iadTKzMBzjvnhc1H+uS84QaRzt1aAU/xtCn16TKaatd6kDOi8O61tjaQ+arT3RtAR1qq4/qD+wbzp7ZpJ8xvEnPBZwyN2y9iSEXPzcWNwg3jHKiD3TTX+rnTQj2d7HV9TDXhL7MMecEp50Heo51tjmeOEabdTD3Lmb6yvEk/XJs5U6fR7K6Lplv5w9q/K2cHeeDSrp80udWbPLMD7fqJ+cCqVdzg0Pj1R8fiIwf8udc4Nic9OP8ofZ3uVQOXROpuW7ZKR/y65zBftrUAfvyEM/x/95LV/7QGr/dRd+Zd8bnnLVR88q6VRtw3lmDlCVrr2ye1aec9tpnnpkD89LGewnfNbZth7ngM2XRNz4yT32ai/Ed81jVIWMd0jWGeWHLDx3e89lvjlU/c0/StzJ+8z6qPjnMGWrcOodVDG3gDW944/4vVWIL2Gc9tmSvjweQk3L2J5k3ZI1W16KrBXKuP3To72TQFlLHPD3g0HXo8sRnrg/Q55Y/sG84W2aTfsbwJj0Xa124LHJuDG6QXPyCPjdKlRPtUuZG6fSzH72MjZw3GWQfBzLkPJCrL/slc0m55lltOacePCRWeaDDg43Ykn6V8ZFvwew7Zn41d3XTjjYhL+dT5wXop2/9QBc/9Zlv6nbzSFk9SV9ivh7degDHcs0e8teNC+P6c3zLH+RcIH2otxWTsW5u6QO71FMG/dLXxTAHyFw7O+VufTqeudZ8rlfGf34nnXydP63xxefS6k0ypI3xgH7pZOt1mmsoh+zMQx2oOXSxOM+5es/Rr0/axPjKxMwa6Eu99AU1Z/3Tpn0l43a6NUZFe32ActWn33nhd+UbGd06Z0i9nCekjrZdDPRck/omL7j77nv39xN92OoL2Wu6kjuMT5tyYvxj1q/jkLWouqlXZdDWvFzfNUf09Zt+tmIn2mgHK3/Iea8NZ8ts0s8Y3qSzWF20tLnQgcXO4vaG4rzTTTlvQmV/Agd0axyo/RlbGfSdfaCMj5pj+jLOoXmol9hnP36RV3lAzT1j6stzsW/l91DuW28SvCYp60ublGUrfurnfO3r8oHUczxl6PLlQ241L8b8gISVP9dkHa8wHz4ksYMtf45Vf7n+YOXD8ayXVB+wqqVt9VHjeB1tIe2Uq58873KA65XJBXiTzh8z8vekex1oaz5dHzjfeq+A8ejP9Zxy2hy6hpD1VT60HvGJb685R+YA1SZlMDdRrrnUvLIG4rjxU4cxyPVJm/bQxcv7o5IxHE87Sb+Q61ZWtcBvravot153bXMuXcwu/7omORftUz91V7LUOuT16HJGPrQOQd28VodqljHqM9UDtnIU/RjvemIn1R/U9TGcHU+/AsMNw2Jl0W79pM7idoGz6FOXG6PeLJA3gTGg069ykrFt0zd93IDczOriI2OK44CO8zhNTqmbdHkknq9qIbWv88tY+uG82jimDWTdqlxr1eXhUeN3ZFzams+qVt21gJpv2nVjxtvyp479qUNbwW+nCyt/iTkfmiM6fKBu+Ug5a4lcfa/igHl3939dA7C1LoA8aj6nkcH87r7n7n3Lm/TTUudb50YsD3TVqXKdvzZwmrVq/FX9IHNkQ5NrQP9VTvCzqiV0eXmkX8fNRx1y13etT8ra5IYw/VXQNe/0BdXuWL/pE5kDv1V/FSvneiimOsTLGlTwKVxbyPmmXbe2UgbyAGKbj7mA44CcetDFgJwf/XW+gr9VXdI3HMqxi2/s7j5QTw7pZf6McW2Hs2d+u8uCG/3tLvzj0YoL2RsBmRuyu1nRrXATcpN0Np1+UuOeJgdv/sS5pC19qXtsTtiom32SeRh3K//OV/apn34rjkHNyRz0k9dkdX2ky2OFcbbmWlnNKecj6GzluzWW/vggrTpdPKjzUe7IOaS/zge6qznKIR/Kzln9le8k4wD6tU/01eWe8aHL4TQy/v5/H/eRu8fe3f+hEX5t41/9hm+5Ot9ai1oXN0L4TzrbunbMTbpYOYeE/mPWYxe30vlPurzqGt+6562FfcarNZMcRzZW5pn1ga4Wxk299NHdp8lpfR6aD1SdantMTG3sS5nxf/Xmf7n77b/xs3f/1//7k1f9ZA6drxU1XzAf8+xyTroYnd/EGFnnVW2g6tYc7ZPVvCpVr9OB1EOHc9r5Pelnz2zSF9zIgvmxN7/rRHpqkXtTVbqbR/jJmV8pxRs50NfKJvVTXt1o4g1Wb3zRl/nXueQ5svnCsTmZgxyqi5sF2KpHbiq26pdzzPGaZ861+qz+Oe9qmj5r7Tq50uml/9Vcsv6Q+VabOpdK52srl+6ai/qpW/ORzscq3ml8JKmbdL6dfxfLOF1dAJut9VljXA/4SIjHZi2hb2u9Sc1L/ZVt1WcD4XxOsxag1qaj6nC+VXv9p9zlVW0zTpWzFquYXT5bZE41JtS44FidW+plbU7js3Ij80r9LiZkfgn9xOYfjrJJ/z9/4CeeFj/tHMuapJxjtUaQedQ4ldP47eq8FafWoua4InNQbyvP9JV63Vy8tz/mZR+877seZpPeM193OWPyt7twuNDzJmJR80FZbyj0tQV+IsbOc/SrTZL6KWuXcbsczDHzR+ZD3DFQ1raOmS8cmxNxzEe/xqdNGT9puwI9dCR9V8wNiMODCNQ3ljr2p8+UJX06j9RzHDpZ3UM2+oc6l9rvefqsNnVtVKovOBTTeLn2Mkbq1nzo40jb7vpv+chrWvNIeUXnGznHwFj6yn7ngcx9ZWz1M36NoZ3zgK4vwYeHPxBkHwcxzdF8tuqCjfqwshX0+XD3OULOjFf9apNzr+Pg3Gk59JWYW1d7/Wcs43TzkMxFGVtgs5LjSdat5rOSc13os/Ov3zpW52Z+kLnAMT67HPPzoctfqm2NBxnTa4BNrhEPYH7itce3VH3ImqScY5L52KYvwLbOm5pQa1n5hYxxTJysBdQcQd2sf+ZgvlvzT/vUSx1iImffcLb0T/bhusnf7uJN4w3lOTcvN7E3ijcU1IWedtww1YY2Sf2U0fNmSllSN3NAdqweQMtDwwcqrWNS9ZXNg1rwIW4+zg3MBZt86MGqjrSgf+Mdqp962JCL+tmX+cOWz9Q1D2qkT8ezbilzpP+VDVgn2eo3h5w7pM1WXQV9bVLuYjqGD8Zdh9Vv6irndde2ykn1AVW35oF8I3OGLlbq0C/I9GceHejkmlG3W5urnCVz6aj5bOVmXrlWj5mLBxzS1z96HPXaAPZSfWWsqgc5nvKhvKDel0Cu2mS+yVY+UOUuh9UzgaPLyzHQX/YZs9p09YcuX/119+rK1n7j6oODPnTrZ0OF+UrOLetQ44BxqgzIuba9/6ovZag1wa7mXH0i20Lnu4uTftPXIV1An8PrhL59otzFcqzK1Nt5DGfLbNLPGH+7i3jT1IcJC7ve2JCLX1tawK6zqTdzysZNvylD6jrmA0S96i8hLx+k5JTxU662xjJG0tXDuslWHYlXOaZ+zhtSnzjdnPgQuR6f9Ev21fHMAZ/WMPWskbWhD12vn/1SfaLf2agDK/2Uc/0Ys+plLWDlN9cK+db1CCnXOOkj85HsU+a4njkn6RfUM/c6j6oPGQe8XthhT39eQ+zV7XKGbOsY6Fc5r+WKXIOwpW/crFfVV0d/OUfoZOy7tZHxjJN66h6TF2zlRj9+eQY6DjlOvz7MIfNZyR01duZexzJu5tblkv20q/rXHDNPbLr8V7arXDvfgo4QT1Z1ADal+so5KqctaM/4qg6gXOfVgR/XiPJWnqs4lZWP1M05AzZec8hxDueSVJ2sW81hODuuXZnDDcObdG4+FjiLGFi8LOIKOtwM3EzKeQNAXfip602YOlWucbmp6o0GqUu/5yudLVZ5pT9ayZwAe+dZdTu2auK5VF2O7u2PqJ81kIyRB1S96lM9yb46rryVGzWytqCufbWGxjhm7seute5NtGOSMcwBVjqALz/QYGsNiz4cT11a6dbeaeaceR66t+hDXr2xrzYJueCDfvMyV2xWOXOOX6i+1WU84yEfUzvAB0c395RBv3DMNQR859xS5sA2/a7iVT3jA/3Xe00g/dpnfpB26mY+nbzKR7rYsooL+oK0rc+BnMdWzWtuOSbaVdscWz2H0r8y+kKfULMk885cgRhS8xVzUz7NOtxCn4CdPjiyLsawBeeQ84bM55jnMP15jt3WZwFs6eDPHIezZTbp5wA3BTeKNwGLu4MFnj9Z502TttVeXewc92aucmUrjugT/8CNaZ8wVh8E6iNv5WJMbTKn9NP1Z6yUu5oYM/UgdT0/pmaMq9fpG8f+lc/Mp5PZQIh9nR/IGkFeK2xhq4bYZ66VrJV+c171MD4Yl/MbqVc9r3M+FKfTzflnH7U/NOdVnlt52Sp3epA21T/UPmLyDPF5kzmra9v5Rr+bG3De5bZaR50uZFzZqlXqQV6PlKHT7+JVvYxvv+fQyenDuec6sC/vX23qmrF/JXN0OWTt81pJzSvjckDOB9Bn/dQcpdYc0GWe6GZukPa1JoxV/0CMVfxaB+cvb/6pN+1e+vKPeloturz1RYwunvkaI3NPf9V3N6/Ol7JUm4QYh962S+bD2Oo5bB+t8zcvfGR/BzrHXKfh7JhN+jnAYvWG4PDG9GaouNhpWfzcBNrygOjsHAfGiMkNlLJj1b7GyRtViOv4MT+ZV7nLBTJvbdCrfdL1r+T0DdYOOr/qEj/f1Hagy7h6qV/j0O/cb6R21eeKvJZpm/2wimmuqxi1VjVHWtGHNhzVv3aQvjq/KSf4rfdK+hDHVrXAJvtq/pB+uxhJjcVR72H7U6/aSNpydLUA7ThqPKDfGOkLcj51bmmHDOgIsv1VdzUncdwWVnNMHylv1db+Y32ucldOX2Ctuvs/wab2d9eom0vmwcHmS9Jnl1cXVz8cos8ud0HfmkLq6os+IO4qH+eXMtB2z2Djuj7AeiT8Fd0ud/TUVeYgXs7BfMB5QOpA+uvWRcpQfcmqDh2MZe7dPCFzUyftcn1xOLfMK/s9z/xo8zo5Xq/RcHbMJv0cYLFyQwjnLGJvhu4GVWZTlw/ivImqrjHy5kxZqj3ol/MuRo7jz3FQpt+5VdlxZci8HdOGfm21Ub/zn3LVty45r06PlsP+pOok9bzGsfW4ntpB9SmZG+S1Es7rNaxx9JuyZAzlvG7G6t7qQGeT1LlVHcdBueZT75XqQz3arVqgU2sP2ueYtknGgXo9cn2gV9cnetVG0hbSD7oc6RNqvC4PUM751LlB5ub8u/UKqZsymGvm4wd+l1edY8rdPX7MXLd8sp7US/uVL+ee41kP/W7VCcyj9jFH+xgHzle1rznQdvnkWgF8rnRplb3fqi7Yl2OZj/nn8yLnynxWZF0g7/kk52W8bh7oZZ6S+a5qnNS8Orn60l+nW/NUXuVQ9Q7JmW/6zLxSlswP8CXoMl5rMZwd196tw5lQf9J0Ebv4czFXGR1tZWWnHg+d7qYEbDt7yLGqg30d50HDA8f+nFvKkHkoQ9XhnIf/sW+mu1idvphzl4fYv6XjOFiTxJpAXg+g/zS1A/WwO5QbqF9lQNY+Y1a/KUPGyPzQcS4rX1DnJNh114XW8dRBhpqP8aG7B0A9xvEl6DDm2qNd2XdjnV7iHCTnkDVJPdq83mL/Vi1qnTs9qL7U6+pXc1CX/i6mpC6tc4KaD+BPm7Stc5Qau9MH+g/VTZAzNlS5q5s4lvWDmmuiHzed1gHSLuOhk89KUUe9rfsBW/tyvNMV64Ntfb5B7av5APXp5rRVI0HXGqcufWK/Oazm0cUyH3Pimqzu+yTzqjIH+jWmY6kLNU/Ha3xl9eQY2dj5PNy699UH/Xgu1d9wtswm/RxYLXLwnAXNTVjlxBuGG6CzEx4A3U2ZN15np/9OB5m4iXHQBXOqsnQ5pY421S7n41jqVZtOX2pt8k1QzneVq/7sy3p1MmRM+09Tu/RX8+9yS31lr53Xsbv+nV/IGJ0doEMsWdmvWF2XJGvG2FY+K3/q5Tj10Uf6Wdlz5Fgnp6/V9UgdSV2oedZ+zvWzqoU+uzlC+pJav5qDPrt5OJZ6KbPZqfVMO/KU7EMv57iaL+i3jh2qW/Vp/Prsg65uUutX15/on1aZ+pjLap1I17/y2V1P7NGBbhxSt6t5ztW4tS/rxzj2jBvbPLvr6RhtysTgBxRkoQ/uu9xvTP0dmgd0sfCDX3OWOmf1rTXn1gEZ8JExtam66uXhuHQyeqv1nDJHkrFXcXKeq/oJPrg2w9nz9CfRcMPkgneRu+DtQ4eFnbKoDznW6Qo3DzcRN5M3UubR2aHHh4mkzlYc/fMwyxs556he5oScOpA+kmPjyMo/ZB6rWqaOsY1rP9SaSsqAPWS/fjK/bm7Q2WWOW/rIzItx5fr2zTl2vh1LezBe6oH61VedF22S+uZb9fQN9Gc+lcyh6lBn+hnvfBhnZZ+5djK5mT8QQ4yX81vpAn6h63cMe8a7t33QxUzSl3Cec4PM4VA8qTK+js2z9q3k6qvKSc6Vsc6n9yHY12GNujhZu1WegH9BRj9zgc52JYM+8eUzHTkP8848VzIH/le1YByMi2725TzwCcbInE+7nsA4gA3U76Sj44FO5pQwvvoMBMazLlBzM47jysc829GzJqlHm+PHXKMtOX2KPpSr71VdOn/2DWfPXe+fv8PaciN/ovaHfuKt+0XNQmfhsth5GAE3Aef5IKjk4vcmOhZttTP+VrxDOvgkb+YEysTIXCXHIXNS7nysYkDG4WGylSusfDGuzw7tM652xs16dbVDl5hdTfVfc6rUHM1DucLY6jqmLXDexa9ypdODnOtKRzIubPnM69fNC7DZ8nm94KPaZ1+VK4yt1kYl4zDezXfVDyuftb/WtMp1PplXsop36DnCpoWxtM88t+7rpMbXLvvr/LbyEu1z3vSt6gZbtat5yjG1WtmuyJwPkb4zzyofi3Phz8LXOdVYUGOkjjC2un/yGqD3/d/zT3Z/7s+8ZvfXv/HvX+1Tb1Xj9GMeW9ek5lx1V/G0S/SRdHqZX8avuWxR/WbtVjKs5gnps9q9/EUfcCKdnhvZc93JzJv0cyBvLGQWuIvec8a4AWhTBnQ9up/GOxvRTrjBurcV2tHmW9ZjfvpPmVj5EzjkOGROVYcYnV31kTFq/ZKVL/vxs6oFoKcuKNNaI/x1sv4g+xP9ZX705fwyR9EOqj4HulsxGa/5AX36gJRzLUCOgXLGTR3azBNy3lD1Oz39m/9qLqKPWkNY3U+VY66BIB97PVJPOXOBtOv67aOFGt/csw+yTisZ0NcGunWQvjkYy7yrDTimDYfgK2u1dZ20NYfqF+r8tp6Bor/UgeprFQdyTLnWCg49lzvbLbnOp/pL9M2R5ymv6l/90lrf/BxRzzyTjAfIOR8O/VZ/kDU3j3e96537Nv1qry3tlp+MVzEvSN3qr9pjU+fW3RtVD8wPPW0hZej82bfyCVXWr7r4q/8FFlInfdTrPJwNs0k/B1is3CS5mKGedzeMNxsHMg+/Tg9WNsQWbjBiruwAO0G/08UH8+Kmr/PQBj+OOW5OmZ8+9Nf1pQ/IGJLz6PznIav5VR+dLOkvZdBf9lc/OUfJ+WWONRevba0Hvmou2qgDmV/WP9eM1DzUQdauzqOSeZqj+pmfct43tU605gM5F3W6uRoDck7Q6cAx1yA55npA+l3lUu2yX/9s8lKv+uXD1WcHNuaTNe3utW6O6dsx+1bzrTbqQY2BXfqCtIfOV81BvzmnzOtYf6KMfXfPVv/Gp0255gn0YXdsTtVPJ0Pa1j6OKndrGdIndDL2df0k6HW5dbFzPtD51I9jOf7c537gPhep49pC9VNlMc+as7rm6r1Y7aXObXW9Uk9/+Yymn6PKuUdwTF9bPqsM6d++JMch7c1hOFv6O3S4Ibw5Em7uXNwsag4WOAvdG8KFznne/HmsbKCLDVt2nkvV5SBvfdcbFbSxXx3o8tNfvoGhr/vJXcylytU/PmsetGKuWzUUZHWrv+rbnLIO9nMtBZ+ra2Q+tjWXtEv9XF/mBdqr64GO/my1M2/Qf+oge90O1RrwcZq1AejkuXgtbKHGRXaekDHAfFbXX7qxLicxZnctzA30C8iZS9bJcQ9Bt8shdaDa4tP8UwZzhm6O+sgxfddnmzju2md8FUPdhPND10md6ve0z1upOhy1VnDofoOU9Wk+cmxOjm3JgK3+ZJUTMnMy/5pb5qWcrfZQfaxyk7QVfeNj5Q+dmuvdd9+9f5PuXLZsnQ/H6j5VhlXO2Orr2Gcghyinf0g9fDCO/5qHKGuXnzP6sQV9WitlSR85F2Wo8fVFPYazZzbp54APmoSF7OJmsXOTg/3oe6N5U+XN401C29kQk4eQth1bsdI/pK4Qg7yxyblUG8kfMmp+9nsOKUvmpWztIP14QOaxlSvn2mWOedR5Hesb7KcvYyTOi1bZOqcNcpJ2qxz1AZ1vSL81b47MWbvOBjp7ZD5oXA+Q+XXzqzGEefqDXMZN3/WDqvOlPflVHXM+dA3Uy3nSrq5FpwuZS9pW/bz3tHWs6km1Nf+UIeNm/8o+2cqZlnHttmJUO8jaGL/m0OVec7Imp/FnDls6snrWaVfzwTcHsvcGaKOdOt01TR95fTJW5tLJUnOD9IPsfWdrjtLNT8ytu48k48GhnOTHfvSHdy9+ycuv1gDStrv2eS6dvMo5fdHf2WYdOhnqdXA8r6dHd/0cE/Ly3BiAfvqEamts1qP9x9aENnWHs+OpO384Mx6470pZ82aEXPjcTEI/BzdRtfHGAezU4yYRdBg79id6bq6qB/UmS13IvBmDlQ35qUuMtE1yzuaylVfnp9aNHDKPrVwdwzZ9Zy5Q/R3jG7J/FQNSL3WAD/Du2kLa1bzMwfpA9Q05R4/c6B5js1UPZPr1oQ0HftK/c6NNuUJf+knfyMf4QZe8qx7UnLocoZsn6HurJgk6acuxugaMmTdUvzl/+455Nphv6kDGXtmae80lMe9VDOns9N89IyF1xPPMH471162N1FOH+WR9ajwxbr2u9FX97p41B/ukxsOWnMgtx1ayeUH6Bfsl559UH8hZP9iqjWi3um8gY8GDz3vevmWNQ47XeNUWOeOlzHHM9VTeyluZse6+rte2xss8ak65hvVDC8rVZ2cD6InzO6Ymrrnh7JlN+jlx1+7SNQveG4EFz0LvYNFrkzcaN7U3CFQ9fXJkzOrLHHiY6RPUyxhiLG9UbkZRv7PhbYv5dzqSc4FOxpbYq9rVepij/eRhDtpbC3VzTNIn+unvGN95XSBlMQb9qzkSiz51Ie1SP/MS+yB1zTPlrN0qn84Gfa+5Oa3s007dpJsn+thpC8q0Hekn13uStYF6r8FWjvRvXTf0yE8fqat+ziNl7NMmybyrX8m5cOQ8lbN+tRbpP6m25mz8bo6yVe9DtYG0r/E7uatd6mz54zmZuVY9wH7rWaev6jfn25F5oav/7OuuOZgTbY6tZPNa1d5nAtQx2tRL+1rbLtfOj59PoD/tMhbQ/+gjj+zuu+++p9Uy7WQVjzw5N2dkONaHz0BttevWNHrdtctrW0n7lCHrDCl3zzNY2WzpbtWk+hvOjqfuvuFMeXJ374l05QEFLGIWM+SNnrj486bhIVJ1U0+fQD83Pw+B6guQ6dcG2YMHzSon9H3wJysbwI5+DnVSFvQy55T1cah26EFXD8fAfCF16zzSzvoxlv0pQ+c7/da8teegr+ZeQa/Wpqu/Y4l2mQc4N8j46HTX2zxllbN6OVbjdnbmfmgNS8pJ9UEs49MmqWtOqVvt0PegbzUXUA+qrn7BeaDrBgW2/G/lQH+1oW+rrlB1kLu5Q9oaP3NxftpKxjDHOgdtocsRanxgLOt3yCd9K3/018OxCmPdvQ6dX8aRa260gp71z2vS2R/LVo76qs+x/PypNrLKhVzhNH6wqb5qTpnrPffeu7t06dI1NhnjmHgekPKx19TYaYt+jknXr12936DLIcdB27xvvb+OteGAjCeHxpHxM5w9s0k/B571+CP7Reui9ob2XOyvNyA3Tt4U0OlyU6Bb4cZE3xw41K05JNpBzYkbs2PLhlbUgaoPmXPKUGsBXcyuHvR3cSB91nk4X2PrO+OlHnS+sw+6vJG7a+MYrdTa1LzT5yo3WL3BlJoL4Dd1a72dx2o+YA51zJzrvDhHN+NVWV9bPmRVq3ybJurCyq7O0/7UqWsp0W+OkbdyZ1Nj1OtQSf2urtV/6ihDFxPbjK8/dGBVN+q99QYautpoX2OnDjlnf5I+1Vn5A+PVa+h4krWCLpZ2nY9aK8Andarrs7OvmDutsn4kc5Sch/0+LyDHVnU2HnVjzGMVe+VHupyAfuBNuvME/R0bL/NNTnNNRV91zH7o+mkzXtcHeS0S9LynUobqkwOZ9ZA/1EKXg/q03ThkjsPZce2KHM6E993zvP0NygLmZuLw3AVtP+TiRuYmSNTlWL0lqqR/YlbdvOkSbVY5dXYrG/qZNw+zKquT0O9Yyjw4T1s784StOEn6rLWir/uAq/XvfHO+mjvnXFN8O8et3KHGqD5hlZt5ZJ3UNW7mkDKkbr5p55wx5pH9iXnnvVB9J+qD/o2t7NgxPlJOPWTHqu7Wmj0mh06HFozBkWs89ToZjomx0gfnU+8tMa+Uu2cPdnm99XeobsJ45iz064N+dSBjKyf0d2vQeRgT27pe03cXzzxTTjJvY8HqHtc+dYlXcVwdOLRmIH0pp6/qU7Kf1vrY79ihZ1d3DWp9sKm6+qGVjCvUAHiTDtUf51vxrCF0+ULnA46de+2HTh/o0799kPHxqy1tRXsw384nsv4qK32oOSKb33D2zCb9HOBNOgufBexN5DnkTc3CZoGz0JUTdPJmxE/aJKmrzEMIvaoLXT7INZ9qe5p5ZB1SNid9G1t/5g7XWzttDsVJuZuv9h5dXQ755WHuJid9AfNDNl84be6HaiHEYlOCDaR/6HKAzCdb0U/th8wV8nrCMXPNOXVxtny4jkSdeh07/W7NdtcfModDOjk3ZNaHY3BIPiYGpD4HsbAx/ure6mTXab0WievL+WBn7MxXO8ah5gB1nXD/pG3KYK7KiWNeW23THvI84+nPPljVLe91sXY5n86+u6b6reu41qeT8bOqe/Vpn7l0MWv/1rxyDol54wsyr0Q/WznhC/I76dXfVrysYdoYS5vqA+jDRnuoa1QyRo5nv9eJuPV6dfG1rfVJOWulv26NQbVPvSrjV3+QdRzOlmvvwOFM4E36vo1FDMq5mJFZ4FX2hoHUp5/zrZ/gpfNHC5lbZ2Mc7eUYu/oWK21ofRCha17Q+ZPriUkcHiiH4kiNCTyMsm60qXesX/LRpvoU8z0md3RyI2BO6NZadGCvX/OgL2N3svppe0iGrAecZq7g/KDWz7w5wHHIuqQNrWOdfpK+0y7JHA7pAOPAeX6w57G6DhyHYlR9IRY2xgfHs6/mJ6u4FePqu9pxTs0zT8gcgH51MmauAX1B5g117JAPWsC+zjFzYLzLGbmzFcbqtenuY9jKXaq/6hsfabu11m8kly6PVW3hkA7jHEA8qbHRf+CBB3aPPnrlxVj1IzVeYt70aw8ZFzKnJOfd5aBdjW8/B33E43N99fxWt8q1PlJrBcZZ+e+uPzbmlHJCPzUYzp7ZpJ8DvEnft5cXrjelMjcqNwMLWllSBm84+h1T5qg3JNDf+QZ1MqfUVQZjJDkfUL/aVaodN/hpcwdzqjqdLtQ4PIA6H1sx00dev2SV/8pv9dnVZSt3/aFzTC2y/vVaZB58gIOx0elkOY2ceUP6qn5X10lSP/OWHMeum2v6rPpirdI/46kDVe+QjuPqEF9Sz7zoSxm2YlR9+/UJ1d7zrLfj2Chnv2TcjJV0duSXeapT9dBhY4COaCfKaa9+jiUrH85FzI1x+2nRs1are109WuX8rwxAHiv7Lvf0CVnDlAG7tM0511hw2lySLg9R7vKWqsORuShX+O0uDz74vKtrrvOTdc8xWOVBTOeqj7quIecth+JUX8YyXmJs2pqHNl2d0pd23XVN/+SYPiD1qy1gR3/WcDg7nr7ihhsm36SvfjJF7t6G0wK2HsKNWXW4kbih1NU3cRLHObqcqpz5KAM6on7+ZH2MHZBHzR3IbasutMbNsaonGSdzTB/KjlU/5pZ6Yu4cW34r6TOxH7I++uxqsaqXMmSclDOPzJV+x1LOnA7JtpB5iT4h7cwD3ZqXaLs1zsE9k7nQdjaOd3U7tr6Z9yGdykrPeVQ5nwXVVrL+q9jVj3r6TP8rGTJuF6t7djkX6OZVSX3g3DkqZ2553cF803f1Ac4l/UDGgKxVnbOxoNYGjAXodm8nMzdz6XwCuhyud1CfNul8qkN7mly0E/NQXtVWqg7H6jOzywv4Pen+dhd9QK37agzor3mA6xHMpSNtUu7iwMpXvR8ztlRb9OxL2bH00T3LHJPqQ9Km2iNTu+HsOfdN+qtf/erdJ33SJ+3bZwq+SQcWOouXB0C9iTny5lCuNwE3LuArdei3D13Qb6IfdbqcoNp1uenfQ5/Jll1Scwf60Ot8MIdax5UePp03D6Z8E5e5pCydH+uV6N/rc8iv+tVn1ZOuPr5lBmNwdHUAZXQynjL5dDnUXJXNCbZkP1Azl8y98791nSTtgHmkjypnLrbVJ9RcldXtxqDqyTE6mSdYny09ZWq1iqG9c+L6WqdKzts1IZ1/6GRi5vqqZBzy955Bdh2SX9XLOVcZ1Oc8bckBOfug+ob0Yf1yLo6lLjhPbSqpl/44iO+8aVes8l/FrPp5z8lWTcC5VrbssOGoMuvUTbc5r/IxLud1LVUbQJ/+N//Uv9x96If9gqtrCozTrUnHsg9qHpBzTn3nR9vJ5FLjOFbzSftVjdFf3V8ZI2VJHxwr/9qlnNjX2UPKw9lx7pv07/9nP7j7gR/4gd0/+Af/4KTnzudZz/mwE+nKDejmALh5vSGBhc+Nxw3ozeFDDVj42kLeKPZrB+nfmx/yBqo5QZcXR82t04PT2onjFe2zrbWAGgtyrik73tWo5g/Vj7G1gexf+a360vmkTTIf2i4WMJZ1SJkDPeMpuymmPSZXwZ+sZMCX8TmMfYz/zCVlUBe9eq9IyoC9pN8Ef7Vu9texKqe/lf6huWR9VnqQNnnUPEC/XGdI/4IO4Nf1lT5Xc1bmwF/aHxMnbZwTpJ6sZDCHTiaGfTm25SPz4j5jnom6xzxHONIfeO79Z/+Kru5dTEm9le/UQQZr4nnHlh1UGZ3MoT63BD39MWZdco4pA/r4e9c7H9nde+89+3qC47TkYPyt6yWZh3Q1h615d3OGHFv5In7WmAPdzjZzqjJozyHI1b8cqlG1VbYdzp5z36Q//Laf2bcPfdBTG9c7nScev3LjQd4AwE3mDckNwE1hnzcD5y78ag/0df2Q/kE5bTrbLi/ocuv0yDdv7HyDAtUudasM6Pugtj00Z2ydZ9av2mUu0OWV9sqJNul75RdSf3Vtuzy26pP6dR2lDMQynnLG1xcoM97VUZ+H2vSfHPIP9q/yUpd5po+VP2Vz01etb1239m/VVxm6a1R1QDnz1G6lt7oWNT+wL9EmdbDn0Helm0OVIXOSQ3HSptp7fuja4jP913lXPca078Ygx2pNMw5rxTFY6Zmz6D/7RJtVnMwHDuXGOdhfdVZvuTt9Wshrr83qOlW26qlc7cjRvmrLHOC5H3jlK6aALuM1h1q79FtzUIZVzbE9Zt5pX8eyP8eyxlDHocsJlOt88r6o/mU111U9kP18Trvh7Lj2KX4OuDl/9zvfsW+fCdx9z5X/ZO/NUW8EbzYWNYsb8iZEn4XPA6jeaFuy4IeHBQ8N/XKDbtmA8TMv0IdUPfzkDYqMTvqAtJOVLDXHVf6Zo/nU+Am6WSOouWhffRlLu6T6rddhlZvjUPOQlCH19Zd+aIlfa5VrAbQ5lCvn2OlTHWzwSatPxmEVq/Mv2Y9erWf6o823bsrQrfn0BVlTZPr15RwyR8a1rTKkP6g6tcZgnnWeqUc+mYc2UPOD7Ev0B5nrSh/SJmVzzPrSQuodG6eulZxzyo7l/KX6r3XqnqmObc0fahznWI/8IW+VT8bvcpGMI8jHrGPHtvySW5eTOpIypH9sGMdXyiu0W/k3FzBH5bRFpg733nvf/m26bOWQdTPfY+e7dU8emrf2dW4ede2DY1DHHcucan5b6xC06eKmL+jqkZAf+sPZc+6bdDfnz/nA5+/bZxoubm8EDmRugrrQJfvz5jgk583GDUl/PZdqs5WXYys9Wm5Qb2zaRBtuZHRTv8ocaaMs6q7yzxiJ46nbvUnKXCTlzk+Vs/b1Ohgn0fZ66lNzreR1r/nZR1w4JlfGqZt6jCOnT3B8FQs6/1D7M6/qj/lL9dXlVHPnWF1zbatfbOtcQH/qd3o5F7Gvm6d66RdybtkPVRfMhZajW19J1e/mmzmA8vXGSX/05TXp5pTz764h1DpxdG9m0y5zUq5zUN/xeo2PyQc6+Zg4+qEfnZUNbPmFmpP1qfra1FxyLGVRn1ZZn51/c9FGqi2Q+3vfe2m/Uacf0lcl6yar+lQf1TZ1On3zVT/rXOvhc6kbo6223Tqo+XHeXe+kywnSl3PTB32ZI6Sf4Wy59ql7DnzIc969b59Jb9KBG4MbxIWdCxiZRQ11weeN4o2RvlYy1JtEezlkg7z1pkkyf0DPvnyTWe2z3/OUHasxzTV1V/nr85g54MO4kP49P8aPpIxvc0yZh+vKZ8b1PGXH0qa7XrSJsc2P8ezLGqxyBcfysB9cW3WN2Wasrg5VTrp4NfcOdDOfPIA4Kz/a1txAmy5f5wad74wvnueYcr0O4rwyt5UM5CKZV8rH6CfkV6/39cahL31srW1rw0Ff+q6oJ+rR19UQzAn0nXG2rjF6+RysZNwqc2ScmlP6VB86my2/FcbVd7zqr3I5dC8D+pJ5ppw5qwfVj3GBMb7qwkY9/dCmnGTdlDnQq/ls2Z523qCt/ZznD0WQNsr4zPGsQdqmjE33eUybpN+Efq7H1rwyltdtOFvOfZP+s49d+a7YM+1NOt9LZyGzeL1xWMQsehe25M2hnDcTN5m+VrIx9E0fPniQJCubPMwBlOlf5Q/04bOS9oLsecqSNjm2Oq950V7vHGr/MX5S1t7606Zs/SV9SvpJWdKGo/NXY9dcsy9Z5UpfriX1sg99PxSw6+LLqg6wmsOWP+j0aDOf1CN3fBxbA1DGRn8137Q5NkeO1Xj3lg1qbt0bYshcuvVfczyknzlC1he9lV3K0MXBr3Yc3TxqfWocyByV67MQVjXMnPRtP2xd43oOmQ9kzVIWYrs+V3FyXozlODbVb9WpoM/9u6Xf5ZK1gE5Gf6uegC6+ch1r08UlT879qovXt4tf10InG0u2bOHYeZuz9tbAfvyI/Vkr5bRNMi9l10RlNaeak9Q55v2hLj6QU284O57+1DpjPuC5z923/gPSN7zhDbvf/Jt/8+6uu+7aHy94wQt2v/Zf//x9/53Ek7t7n7aQWcR5Q4I63CTcjOrXBZ++VjJwc3LTQRcP0PemzxuVNsfNR//coN3bLX1lHpB+ujhgvvYZj6OOQe2jXdW1zmGlK6tctvxUn5zjA+iXlNPfjdRH0o/9NXbmyjXkw7i7luoDfelPH6m3qiVU20rN+9AcBPlQ7oCsL/3X3LXd8tPlid5Wvql3KEep4/jID0VIfTAOeVhj9TM/7Vf3MC2oy0Ef8fS7mgNkDLieOK7LXCuMr+rM+SoOZI45j0rGyLlu2YA2GXclQ+YDxHVO5pC6xs6xzmfNMf2Ccj5L9EFbQb/T0W/6FvryOqXMgY/MdeUbcj7a6LPaIPuPRlkH+skDsvZbctb8kC2s5qxMfs4VMsYK9NVT7u4NIR73gaxibM3JWN2ayHmt7jVkdIaz59w36fnbXb7hG75h99KXvnT3Ld/yLfs+eMc73rH7jn/49/e/S/1O2qjnIubhmDeIOE7LTcLNgqyu+qmnjE/Jcf1AxksdSD1wMyCZj9CHTtohc+NWXTk2DtR51bE6P/p4gKS/RF3zQq/qMrbybS5bfjqf+qCfB5c5qpdxUobT1KfLHdlYGRvs9xwytnLadjVOPclcOLBfrfsk8z40h3ocyh050T9jmd/KT9rndUD2hxz6Mt+VDaTvOi/oYuND7HdMzIc8EuNnP33Yd3nl9euuO3Q5ql/v3dPGqbEk56Geultx6F+tBWPTAn6yhhlDOpsuLqzy0Wf6UnY9QY29irXK0WvhOoeVj5oHrWzpVH39c54y5NwlfefakWqT+WfcK7+C8anvpINjoJ9cCytZsCdGp5N6mdNKBuUuBq2yzyT1lNNO0p546JhnUuN0c5euvs6Fc2zyM6qb43C2PP3OOGP87S5sxL/wC79w9/znP3/3qle9avc93/M9u+/8zu/c/dbf9gX7cTbrX/QlX7qX7wRY/MDCZZHXGwXZcWHhc8Mc0qs+7RN8EH/LBxgPXfxVGPdmTNJOHfXMPUn9VRxwXkmOAb47fedZY3e1SBkO+Qb6HeNBWv3Qgnoc9HVzAn0B8mnqY0z7GCcn7KWLnXkDdhnbc227tzepj17NRWquqUubGLfK6OUcuvxXuWfOCTqM5bw6PzUW0J+oa//K5pgcHUO3q5F0MaSz1W/FWJnXobdx6nGAucCq5uhmHEBXkLu3c3V+xl3Nv8YxFnPq/EPmIdil3iGbjHlI3vKFjK7HMWsJeZUj14I+Zak+oMtjpcN5XScJ49p086aF1DPH1Kn6kjbIxGCD7nfSQZu0p804nazeVh0dpxVzgpSzhl0tAL+SeUCugYy7sqc/faz0Uidl8jT/1IccS33nZTucPXe9/zIn8rnwqZ/6qbvv/d7v3cts0H/k9d+1+7CP+Lj9uXzCL/tFu9f/yJv3Mpv1hx56aC/fSvgqzvWW5k0/c+Ufy/Lh4MLmhulwPEldFr83BTccD8i8CaX66eJ1sQR9xmm52bxJkTNmYgztkuojb/pj46hjv/N/57ve3eqKfp1vza2C3pZvyHy7+cKx8zmkc6g+Gds5gv2dX1np2J/+tsgcpLPt9KDObasmSeaPTV6LVfxj/Vc/NZZyrVuXS/ZB9Z0c8pHyVgxY2R475/qMkcwRUoZuXkmNU3E86eIdO/8ap/Nf7eqcOrr8sbV/S64wtqo3aFPnaT/nK7+HSB/Q5VF1kpX+Ktck64ysn04XVvryR//wH9p99C/92N3v/F1ftD+vdelsVqRdnXfNr+al3NnVnLY+15Mas1JjJXUuW3EA/a5Wq/4Kei9/0QecnJ2eG9lz3cmc+5t0/8Ho/ffds/uO7/iOp23Q4Xf87qfeoL/+9a8/kW5v2OzlDYTM4U+cnh96Y+JNwTgPgbxJ9MFR0d4W8FFjgeeMgQ8bqDET42KX84Lqo+ZKy00vGcc8wX7n373dhfSdsYH+zC9ljur7mDdvnZ9j5yOpI/ixXfkznrrieedXVjrpb/UGJ0G3zh/qenbs0PoQ89qKy2FtGLevyxs6/x36EeUte3RqLpA2oO9DOa58HBqXle0xc8b3sesfWVuubdWnTTIOdOvk2DXSjUuNI+lbOfMF59Tp6rfmDfTLllx94YOYW9cG6jy1V97K0fllvpA+Vnl0/qDqGwO6XGt+h55rqQ/ps+ZJbo8+8tTvSNdGX4BNt6arDNqRQ9U5lBc4ltinX3xk7eqckrSpMsfWtVaHo8bp7KDTga0cAV3yGs6ec9+k+6sXP+3TP2f38R//8Xu58uIXv/hE2u3e8pa3nEi3NzyI8gagBRY6C76eQ9XjA9NzbzZJv52cm1ly0baLVcc454bjgbAVU7yBnRc2nY+0B2y6OJC52HpUql99JplfytD5Nj5kLqlT/Rw7n5VOncfKX+pVuZv7aXWclyjXmKyx/MCFtEWHhzdkrZhLrUM3z1VcWvxpxzms8l75h/TZyVv5CXEZF3Q8KjVH700OY6ziduMcYL7U2/4u526Oyql3mjqu6r6Kg8zaST3y1o+51HgZ03P7uhgpZ7ytdQKZR8o5BlvxXPdJ9ZX5Q+dndZ1Tp96Hq/lVO2VrvKLOuV5/cLzOCboadutIUl9/K33mDg8+76m/OOr88l7gMEfoZGsCXQ1dQ6u8OMD4tJkL4Hfrcx3SHrIeKeeYKNf4tXYru5VOzbFS/Q1nx017k+4/IO14/gs/6kS6rPfwwyfS7Q03NDcw1MVbb0zlbpEzxg1ebzrIGygf0tUPNxBkXHW82R3joI9x7bqYQF/6tIX0Yf6Q9uj4g0SiT/11808Z0m/mnqTPlX9wjAcb19DzqgeOAf3HzIdrxfo4NA/6cy6dHj7rtd/Sh2N08Jvzh+qD/lWdIeMA/Y7l3Oo8IXVrXNEuwaZeNzi25lXu8tOW1nPGibVaq0nmmD7xQY65hjKuco4bA2qO9Xw1X3MR61brWH0mVR9qHGDM9Zp6+qTP/lW8rsbQxQPk9AvI3TqR7KvjylvxuhqBvo6dwzHXD381Hn3HXA/o4tAm6aOL5dE9I8FxYKxbw2lT9bu4wBzvu+++a96mwyrPrMlWfaDq5AE1L+cB6WuVC/rapAxdLsZNGZBrnqvPhKSzqzi+ypUWaNEbzp6b9ibdf0DacfkWO5Eu612A76OfFdwoLn5vgG6h82Cregk3WL3pIfXR4Sbhplr5MZ463lSZB3T2XUz6nIfgM+cDmX/22ybmol9k32BIJ+Mr5y+dP+cpmV+O249dnkPnc2s+GRM/6K7moZ+UpdPDXzd3SP1jdHIs5+/YyofztCbqJakD6NS1Ap0evmrszCf163WDQzVP310cZdGWuImxJfXIx7m5GTdHY9Q4eV7HJOchna/VfLt6Qe2vPp2L46mvbsbR1msB2S/6zWuQ1Brnc3brOup3dX87Tlt1IcdB/13MpPPL9TdvcD5d3nKMTnLoehyKU3PudB2jhbw21V65+oCVTfd8SIh36dKl3T333rvPDw7pW5OuPtUudeBQXs6D/lV99SHaQNprpz7tSq55cn7aNQLpExyXTkafODzPhrPn2t3KOXDavzh6J7xJf+4Dd+/bY9/cdXreJMKNxo3AjaecerT44qbyfBVbndVP22kLPjA4eDgxlvlkLuknqfaZV8qAD0DfHLX3yFpw1NidP9jKD+q4/iX1pPNZ43cxs360oB1tymAuWW+gzTdToj4HOl0eqZPXRhyDlQ9AZ7WepNM59h7BV51j5pP6kHkn9G2tHeWtezJ9G9dzQM4YkPml7HhX+9q3lQvH6t6qevQ5X3GsYn/nG3IukH66OJUtv9rZTyvEsMapp13KxoCaj366+XS63RrPdZk2dT6CjC/1kD0y7+SQjrFoE20g7Q7FAcYF+Zh7FVb2oi0tdDE5p9aHPhu5trxJB+eVep1Nxks512LCeF0jtW6gL/2t8gd8qJvPCuVOX1ZyxsaWdXmofmDcLhascjQW+sYZzp5z36Sf1V8cfeUrX3n1DyB5XNQN/bsee+LybXBpL3c3FIu7HtzQtKBevbm4ERjjnIdE6nHjaC+r2KA/brYt21UOYA605l/9aEcLmTd0cvpBXzl96Ue/Xez0180z/XGok1QdZP2saoceZPwO5uAHfNZhay1A6tMPjom58sED+Ovy3PJLf/o55AN7xrs6ijp55NyVq445VhizVc6cO5ynPtNWmaPLK+uyuv6QMfSX+tWmq33t07bLBTnvTVjprdZs1UsZ3926zLlUu0P3E+QcYfUcqXMBbLl/PE+7lDNG9QuOk6s503agq28OY0v1n3FX68WaHLrHtu5lqDXSTjmvx1YcWsh8PYwBOTd96UO79JFyl2utj7XuYgo6jz76yO6BB56616CzqXWpz4dcJ1U37y1jiDrV96H8tcm4KUPGXNXSfDK2fbSdv5pv3t/pU8wr80VO3YwznB3nvkmvf3H0euCvkr7uda/b/3pGfkUPx2d/7uftf6Wjv97xovH+3X1XFzA3EzeV59xE3iTCwgd1oN5cjjmeetqLejW2cENCfTsJqWsOnHcfoMr4yHl580O9ebHJvKpcayOMm7cYv9aUfg/6skar3E6jkz7VpeWo87J/NS/6Ml9z8BwyB6j9nhsHzA8yftVJjJl1Xs2z80H/Kq7UPuLVddrdI2nHgX6iDXQ5J8ZJujVU8+rqsiJj4PMYfbCe2GSftlWP87w38wD1AJkP5Kxj1kyqjK+M361tqHbarHQga4y+urSwmoswlnloJ1xX18pKx9j1h+aVvpgX41XXvM0v6wHqg2Ppo453140WjANZoyobP+2VYaUvea221oBz6WQw32Pup4ylnXBtH3zweU/7DS/VBvAvW7Gg6uqTo3tObM2D8Zp/teFcOv2tWnbPvUQfHoCeINNf/Tk/SfuUwXyHs+fcN+n5F0ePoX4n3c35W970g9eM/bW/9N/sN+n/2Vf98ZOeiwNfd7n88+bJ2bU/heY51JsBmT4WPTcBC185x7mRoN4soA5txq791Q7Uwb++1fMmBvQqOS9QTh+SeXUymKs5OY4vzsGxfNNh/tLFz9xqjWVLhzb11QXkOhdQrvMCZVqxz7jG2+qHzDvpcun80lpn5w2cH/KRsqiX83NTKbkG8hxyrhk/P+QgbdCt9TA+RyfXmKyhLq/Veun8HnufKuvXGNmX6M9+8pKMnXp5ZB2zZjm31TwhawVezy27jJNjtcagbtan8+tcpdpBzbXzXckcO/0qm9dKd1VH9XOsy7XmAl2s1fVTTlZxVtcPspZbawBWcoKPrXhS14gtz32+k56/3UXSxvhdLMYP1TDJeWtH30ofav6gDWQOUPXRUzdlyHyyH9Kvcp1btUl/1Tbl/IzFhh9wh7Pn3Dfpbs6v9zvp/+g7vnv/KxrvfuijT3qu8OEf8Yt3n/EZn7H/S6YX7WsvfN3lyd29J2dXqDeW5240XPjADcKip0+ZG6KOQ3fzgDeZdPG2bPVv3KoPKQsxuPF5ABgzfSSOdzLkHFLGj+foOqe0O+atE4e+nK8coyPoOOecex2zL+fSyeYLGbdbA3VuWfek5qGMXY0n9Gd8qH44ttaIOqBvzvP6SOpC2pkDfcbXR+I4/Zkn5Nw6mVxWMe1Hhw+jbn1B9asPdY7RZxyZGN1/6YLunqp+067qW6e8jsbNHLrYkj7UW9mpB+ZpLmAOVcaXpF99gDorO6C/Ww+ZF5iT7cpnlc1LfZ9JkOOJuvoHz+u1WY3BKpeVDJ0vDuadutbZeoBxIe2x6fS3ng+0xNt6Xov5MmYOnPvbXRxLO/TUNVadG9AvqZNyos+0q/4rmYuscgD1t+on6OX8V37Nj/FDuUK1lWqb8Yaz5dw36W7Oj/1Oer4tf8Mb3rD75m/6ht2v/ORftfugB6/d9MILX/jCffvGN75x314UeJP+7N1797KLN2+clHk41RvCc1plbog6Lt2NpC0x8ubFT/pd2UrGhU7u5pQfUumj6q5kciYPPgCUzUvZc+cE2X9MrvpOHOPhCOlT1KEFcsj/VG4/ZJ++cl7dHM3Xc8g60m8M+yDr3uWobsqAnfGNmXJS51h9KWetc45A2+lVubs+xPOtTeYhjrMOHXcuq7orr2JK9ndzrn6TY/VpPVZkza0Z5HVMOn37tE27zgd69fr4g0TnI8n4UHPRn/cc6OtQPfPaYa9d1c/5Op592AMyPg/lssoL8LsaNxatcsaCem1Sr5tHF2sl64u2xtFfwjh0OWOf1x+qvjEkx82ZY6WTMfOeBnz/9Jv/5e6lL/+oa+JUu1wXifr0H6qhvvRb9WlTH6qNuSSZQ7WHWj/v8cqqzuheT65p08mVjD2cHdeulnPgmM356tcu3vfsJ/ZfaXni8f4nNO3e856L9RNcfZPe3TiQsjcNBzexN0vCGDdHjmlDPzeP58INXW9eOWQrOa5sC3VO6BEz0e9q/lXGnjkqZ004an1qn3PJ3ME4nFMbHvrVLxgX0nfVqTBurMR8AJ1ujqLuyg9zIofuuuhzlWP6rHbJoXpju/Jlf8auc4SVnnQ2ScbM3IRxD0BHn53shtOY9K9qoN+cM4e+urkeo7+qe8qCPWAPnDufqgvGZN0n+jkUG4wFyNrSHrNmTrtGsO/6sdef46nXxQdturHT5FLzqvFocy0l5JDXoIsFmSuknvOHmstpryPoK20h46RNzVmdlT593bWvPg6tD/o9yJF83/Wud55oPBX/2Pqmr9TragjmY4zu82NlAzWXzAFq/SXrgn3GShhPXf3eSK6Mu5ZTrhBzOHvOfZP+j/7B39v/Q0/aFfwlUv9B6Bd8wRec9F7+yfDJu3fvfvdju0/5lE856bmW9773ytvq+++/eN+FcvGzcLlpuFlWcoUbwJul3ki+Scgx0MZz8WbKG1ZfPBCg2jpefSt7k9J3aD7Vl3qH6gKc6y9zAOX0zYOoxs+56S99Ind+q5+VjnrO09yZB332W2tIu5Sh07ePFuo1sA9Zna0caZVdT9pJ+oasbeeHNnMwbl7bRLutNbCyoeWAzLPLSZl64k+fnex5kjXIOKt7p/OT+RzSr3VfxceeY1WrTjdzQJ9zcCyfLdDJ5uuRrHI3LuT89dHNwZy6uSXOBapejd/N0xjd+qswlrG24oFzFuPTmvcqlmRNazz91RqtrgOkLw7tM6+ch+tc/dV6M5eqn3r6RreOSadTYzIGnHMtn/vcD9yf2w/4OZQrrfKxNURHPXSQOz1Imy6XLo/TfL5XvfSRP6TAjeSaOacsxK2+h7PjqZ3ABeU5z3lg9w+/4x+fnF3LvfdeeVt90d6k5z8cZeFyg7CQj/lpVLwZ6o1EfzcG9HNz5c2d8ABlDMxL0hY63xX69LGaDzr5wDBuV4tDdTFHHiLmY57mgo86f8Y4nH+tTfVba6h96nBAV1Pssn72VzIfjs5P9nWYB5gXh7l2vgU5bSo53618Uq6+Vm9wALusV8pbNpAxlDOPKnf1h+4a0IJzyTpA9acebF1ToE/906zHGl+6uekfqq4QsxvT1iNjc8ixuUPGgfRlHs6B86xZtw5qzG4sY+Tc/GEzx4idOXT51BgpwyoeqAuOAf2rWAl+qGmNDWmfaNOtocxL+8zL8eo79WUrl26NZPytNdTlaCzHgHn5Jp1+fdGe9jOpgl6t4SrfrVrnHMB5AP2Anjkhg2OivyqnHjL93XyAsa1cYfXMXsmAjJ/h7Lnwm3R4wUNP/5fb4D8Y/eiPvvYfld5q+LrL5Y/gaxa+LaQs3eLnBkKXxa8syB4JN6c3bfXHjZcPhUrapu+a2zGkDX71x5E+jAEpS/oBc+Q8fYI6x8w/fUL67WoIqSOpax60XjPbjrSF9GOM7Mt55tyyjw8+qL5zc1LXU/Wn3M0380k/1VfmwVjmkj5sq8yxslE3c4Vac/S6+qfd6hqk36xDxpdj/GUu1gddNhKgvb5cq+kT2fg5x0R7WuhqAulj5QsydpLz7HLPDYcHqOP6yDHJmnF4DjUmaN/lU+dG3qJ/ZUkZuvhwTDxRt8Zc6aVP5Hx2Qd7PK/La1etIm7bVV+e764OcW7K1RjKnbjzXR+IcOIC65Jt09LH3PNE3LbHR9Xqt6GoI+pFOz3HidPOAHDMnsN9zfHU1Ume17tJOtnIF8zBHOK08nB0XepP+kpe8ZPe8D3jW7p/+X9+7e+KJJ056n+Kn/tVbd7/q419y+Sa98rvYLxq58Lmh6k2WMtQFz83CuDKs/CTeqN0N5NjKlhudGz79A/bd2ErWpiMfJOjbHusH+/RhTcxvNf+063LL8ZVe6gjnxM7cseOa5ducnJ9oa94czMfzreuRce0zFqR95qCedYOcZ8rmlDJH+oHqK/MAbHKe5p21yLUNh2zoczMIxs2aZy7YdfOtcSDHgX6OzPFYfxzoosOmonvDl/bI2nFAyvqqPgCdQzWB9HHsGu36ocu95rZaH9019xDk1fXp7Lr5d9TYtBxdPhm/XttD8dTj6NZPjQXOD5DTBwcx0r76EvWrDOh7XWGV20oGfXLUeoLx6nwAvdV4zs8cM5Z2jOV30rHRlzr6gYyjrtdLPdok49mmH6l6yqs17rxqvO46QMaseec5rOwk80s5yXV+SLYdzp4LvUmHf/O3ffH+t7f80A/90EnPFfjNL3/3b3/z7t/6HV+8u/vuK3+G/6Lg111y4XMD1ZtMlNF3wWtLu+XHNyrgjUkLefNUn6CftFn55zhmDqCsHWRuyjyMGPdhAsf6wVbMyxYdbercwTH7tnLr9DK2ZG3U71DHeJB5e87GifP0C3k94FDc9AVbtlkrdVZzTh04lAeoU+dlLbb6tsbNhYO+pOaivfqScRyrtpA5wDH+YMun/XWtYntM7UFd2kM1kdWYc9If5Lzt58iclTvSHl2pfnOu+M85WU/nRbyqB+jWWkrnE+hTv84TMn7Kjh0TDzIm1Fgcx9YUDvmqsvV1nt1/sZFDcvWdb/tzrJuPMvkg1zGgxV/mCNnmm3RtPUBd88qxlGU1t5QzDnQ6uY6zrurBMf2Qz/xaI8hckm7Oh3JNyCM/h7bkmvNwdvRX5wLxqj/0+/a/4eWVv++3XPP70D/pkz5p94mf+Im7L/+K//ik52LB112AhSzcKNxg3GhV5kCXhc6CB87z5pW0Q1c9yBtFX95EiTGh3lz0G6ParfLvZPI6lBvj9mNbfXEAD5L0080nW9B36urnmNzkUGwxd3X1Tws5n4wHOSae01qTGpvc6IcaL6m+xbjY5Nz0BfTzYajvVZzuulcd46Xsm0h0t/rAttZPGF/FNz/oxjMO5FpJ0KlrtNPd8lfj01r/br2lfieru6LaWAfXK32QOVd/jnltwPyqnPEkfScZL+dqH+O5zqXmIdhz3q1ZUJe+GhuyL6HfsZTxwzP2UDzBLtcPpE7mknJdY+ZwyJekL9Dew770t5JB35znRhK6uNapysB5zQ/0yUF85m8M+3yTnr6yTubMsXUPqgM1f8kctYeVjnR+Yavfenc1ytxTlrRPHehy7XyIOcJK7u7P4Wy48Jt0/mjR29/+9t1P/PS795v1u+66a3/82s/5dbt/9s/+2e6B+559onmx8OaAXPzcENwYnKcMLPpc+OANtfIh6unDI3WEPvxxY6VuQgweotU++7dk84HMjbrw8DBeF1/7jJ0+Uxcda6M+MXJuSc0tP1xqbnJsbGTf+ohy6nVxOl8p65fzZFXrLV8pUyewBom+7N+KA9eTC/GxoyZJ7Ut9czWvHIOarzFrfl570Aetcl7L1RjnkL6rrnlt1SfXQ+rRZ4zOFlK3m49UG8Zq3nU9dP6wod91LOpK+sUufVS5+so5QVdf+vJeUleZQxtIn9rhK2sv6QPM1/okabuKlzrgfPDreM5FUl5dq0O+Or/OhzZlSH8r2Tj6ZEzsr3FtIWXQJtnKC2i5D7vf7oKe5A9z+hDlrMWqdsqJ9lVX8Oe1ot8jx7RJOyDX/AyuOlvzgDrXQ591XS1SBttKjTWcHXe9n997ODwNfhC43tK87dH37t7x6OMnZ0+RN0QHN/I73/Xu/WJP3bwxtnx09tkH3JzK6uDf/kM5ngZj86AB4hzK69j5Qc4FsLVWh+bW5Qar+IdiS2ev76TLb4vTzKeLt+KQ38oqzvXmkvGRa1vr3sXpxqTmmLkB41v1N5dKFwsO6RqPD0zyoGWjsfKX+R6SnUOdj77VM7Y1APN2vumj85f6kDY5F/WOIe22YB7UDKpN1sKxrBVkTjXXOoda29TvYkGNt9JLjq0nVN1Kjm/57Vj5rBya0yrHWs/MZSWDfrB/wxveuPusT/3l+/OO//BVf2z3xV/6ldfEwl+ud8foM9ck69XJlTpfznMOaVdrwFjqdzFW46t5rHSg5pqkjwTdmnfmY34f87IP3o9dDzey57qTefprgeFMYMHyk6pt3hAs6O6n1fxplD5uCsDWAzp7dKt99QnKmQ9Uuy7GSjbPirHRq6zy2vK9NRfnk7JU34CvfLB1dslW7HqNa+767tYCrHx1fmE1H/o5R3/L16E8jrkGGaf6OU0uCbFAO8i6V/3VWOZNvwdkbpI+MjdtlGvexqFVPjRHIB55sP5oOx1RD/9bsnOAnE/61kb9Lm9Jf/kGTp2URZusyeq6d3JiXpmj65D8u/iQtdAm5wvadvZ1Dumv6nexoMaret2cunxWNvVagWO0QE1z/Sc5n7wO6qUvZfOUQ3Pq4kLawSG5+sH+JS958e4Lf9e/d9JzLfuvxn7pv7/PBV3WO/PzXhHzoM8YWQtZyTlX0EeSc0iyBoyZl321nt24cbt5dPFy/lXHOHndunWReUPmY42Hs2fepC84izfpeSMANwOLPxc6Otwc+WYob6ZqU+0lY2kP9hPDn6aV8bOyOw01z/QJxuve4GVeXfzqC9Kmcszcqk/Hujqv5mJsbdHLGtgnqbei+koZv1k/x6HzueVLeQVzdD3CId2u3slWfM5rzTqfqzjZD6v6H0PmVuOt6oZerdVKdwttVuvuGMyZ9bGqlxDvUK7pr7Llv6sJGPOQnNcwqXFStxuD2p+s5qAtZP8h/a1YkH5Fm2NykVWcVd1X1Lw5P7b2spVf+kt755rrdCWbS/rR78e+/EP2Ywlv0V/xpf9hmy92h+bRja9yAfUPzbX2g2Or53oF+608YSseHDsXOBSj5ouvi/ImnV8s8qY3vWn/V+n5Y5m3M9f+eDycGSxYFnMlbwhvAn5CRV8c8wbwTRakPTb1J3/QPvvzJ+78iTh/ak9/p5Gl84nMBwc3NK05SOaFzxqjI23AOLR1bl4DfeszbUQ7SB/oqN/NgXyJg2/tau4ZW/RZc6wy4LerlTrH+kpZtHVOxOmuQeopWw+oY8fMC2rNumtY+4gB2Q/Vl5hTl59kbjXeaj12tUo/UuPbJ/qoc6x2Xd5izuh19Up78kM+dJ/lB7H2nf/MqasJHCODfunv/CSrOXY2mT+sarSKeUg/oX+VU+d/VU90VjaQcfCRuslWPsmh2lc/qdPFrfWCnOsxMuRnIC1j9W06b9HZoEPmCciQ/creDznPpOaiXPXtX821xs3PReYH5tHVFZt6PUB/tF285Ji5mIOkf9AH56mbfm81X/5Fv2n3WZ/1WbvP/uzPPum5femf9sMNw4JlMScuaG84Fz0tN2vtB25Q/WjvTcGNzQ2uDUcnS9oq+3CAzPm0cvqmX1JWRz3JPvJNv908AH3rBcZBT1/6SR/KjuuHOldZHVFfvfRT65CxVjKkrfChoS7oUzlRFzpfkP628hD609dKT9mc6pj2q/jg3Oq80mfWFjIO0F+v4aE5pt+ak3Q5VF1axg/dh5Dx6cs8jdHNscroZYwEe32sfDmXlFf+oK51QK+rDzDG8yz7kmPXA31bOaoH5gXI3fVwLNHH6jlYWcWrOUKnw/jKf/rOcW2OmVP1v9KrMcBacFQ/wtgxnxmgL8jYYD9syd7X6ffZu/fuW96aJ3/oP/7qE+kKxnQugM8uf+tEm7JkLsqpQx8HrOaa/cj20+b88Jl5IXPt3dDXPEHf9NV49CWMr+aiz5RBX4KdcUB/F4VH3vdh+/Z5z+v/EObtxGzSzwH+4ih0C56Wm89FTx8LHLr+7k0WH3KAPjdK3kA8gLx50lfmoD3gg5uLWHnTnVbWt37Sp3rqZC4pk1fqy2oePLCcL4cxGavzyRopO27d8Zty9Zv+8lplv7mp38WFzlbSt3VJyCfXwFYeOSdZ5aF9ypJ63bVVPlQrUDY/c63zTP9iX+03xtZ8senyg1VOh3SzDl1MyPj6om917dTLXLu8ta05d/l39ilD9Sc1T32l/6SeQ+Z27HrofHe6Obc8uhiOgXFoyYl+fSWpV+N1+hkrde1TlvQP2OS9oA3HoTmlLFv5iDkYt/Mj1Krzk3I3p6xTjtfYCbHyMxCe3N27b5/34EO7T//Mz93Lv/SXf9zu9/z+P7CXM7d6QJc/bVfbnIPrlnNlyHms6mv8PFbkeKff5cm4scnHHOjrWM0FVv7NAZt6vfDBdboovOvRt51Itz9PvyuGG8Y/ZgTdgmeRu+DpY4FD3uTZ740H2S/4Qgdbx/KmqjmkPTHrWy9uvnzwKEs3DvqmL+OoD+ZCbse8vdqaB/3aGNM3DulLH9YofUr2pVznkuhvVQfImJ2ctrRAyxg6NTZjtW8rD1nFR+bYuubqcNBn/LSBHKtgW2Oe5o3WSk70q1zjod/ll3ZZs2N0c5z+rRpLnitv1bLLO33UnKXad2/haGHlTxxPX3mfpb9OhvSLr2PWQ6IepK9OF7prsZUT/elrpZc6NbY5midzWtX9GP+pDzkX4xx778IqH1jFTdmxvPZdfFjNCcjnmOe/mL/4+fqHv/q1+/aL/+BX7OcF1Vd3b9XPCCBG1hZyDkC/Y8rHzqPLw3pVWaqNMesaYJzYeV/Sh4xu9QvaKqfP6h/MBeo88e3YReChD7ryJv2RRx7Zt7cz8w9HF9zoPxz9jF/9Kbt//v++/qRnGIZhGIbhzuXFL37x/h9tXg9n+Q9H+WOXP/ADP3BD+VwUZpO+4EY36X7lhZ9s+al02mmnnXbaaac9uxY+79d+6u6v/I3/dffCF37o0XbTnk/7kR/21H9VOC1nuUn/tf/65+++4x/+/Ttikz5fdzknWLQc8MTjV/4z0LTTTjvttNNOe/0tn6t83YX2f/lb37j7kX/+/+z+m//qT+7H4Fg/055PexF49zvfcSI9xfd+7/fuXv3qV+9+22//wt1rX/va/fntwLxJX3Cjb9IffvRdV/+ByzAMwzAMZwffkeYtOpt0+M7v+ee7D3/RR+y/H+33qIebAzXnO+wX5fek+yadX8v59re/fb8x/+Zv+oaT0ad4xStesXvNa16z/33qF5V5k35OvH93337hwrTTTjvttNNOe3atb9Hlr37d6/Ybdzfox/qZ9sZbal7/ke2tJN+kf+onvPTqBv23/rYv2H32537eXobXve51u6/5mq85ObuYzJv0BTf6Jp2/OMpPli5cZP6l9TAMwzAM1099iy6+TR9uHm7WL+KbdGFz/k3f+PUnZ1f+IulLX/rSvezb9ovKvEk/J/hHFPmTJTKLmcNfhzTyyCOPPPLII59Orm/Rhbfp6lSbkc9Hlov0Jv3ht/3MiXTlKy25QYeXvOQlu6/8yq/cy+94xzt2r3/9xf1NfPMmfcGN/FT32KUndz/x5nfsf3/qO9/17mvepl+khTwMwzAMtxu/8d/4tHaTDvnd9OH84asu1Poifye94xu+4Rt2X/iFX7iXv/M7v3P3mZ/5mXv5ojFv0s+Bd1/epLMZ51+f56acTTsLmoMFzdv2kUceeeSRRx75sMzxw//8B3cP3Hf37lM+9dfsD/jET/zEq+ev/4Hvv7pB1/a0cUY+Xgbai/QC0u+kP+95z9u3HR/90R99Iu12P/qjP3oiXTzmTfqCs3iT7nfQ+f4cb9Q99wHCwh555JFHHnnkkbdl8JwNonzyx750941/+zt2L3nJi/fnvBzrbIX+9Dfy9cnAZj2/KXDR3qS/+EUftHvDT731pPdavuu7vmv3WZ/1WXv5L/7Fv7j/WsxFZN6knwO+SXch8+dz2aB7zkJ3sY888sgjjzzyyNsyeM5nqn+HBB544Dn7Po5q6+euOA4jX+F6ZI58e36R3qRf/U763R94pT3A/ArGZyD8sYVc1JDnvF3f+kcYMz7jMz7jMz7jM37tuG1+nj722LtPpKfGq17tn/bGWuC/aPjVF9qLwkMf9GEn0nE8/PDDJ9IV+O0vvNnnjx/damaTfk74e9JXDxp+4u9+ClVnxmd8xmdcZnzG4Zk+Drk5R0+w43CcTaN9+GUjSSuM88OAetiN3vF6QP35lkC9Xrea/O0u1wv/6PS+++47Obt1zCb9HPigB++9vLQv7eXVgwZY/Cx8bgZkqA+jGb814z6cOLyWkONwUceBsYtaX5jxGZ/xGT92XB3w+cdmMlGH8fSFnBtJx6dvu4962ucvwrAvcVN/Ubj6Jv2Jd15pD7D6usulS099tt4qZpN+Tjy5u/fqg4XFy8PG88SbgUXveOrM+K0ZTx2vJbAhdpzrysPpIo7LRa2vzPjFGQfXD+fP3r33wo5LjtPvITN+54yDrTr5vXQ+YxOej27yHetiTF/fB75Br+NVz+t0UTjtd9Lr113g/U++Z/O3w9wsZpN+zvBQYfGyiJFZ9D5oJBc/m66qM+M3bxyqji06bIiBPq+rXLRxoZ8DbnV9Z/zWjkPqcLCJAXRcPynLRRo/r/o8k8e7MXCjC7cqP6Bf2fHcmOezEHg++vbXMX7w05Yf+JA57Me/sv2QOnBetmANmBvtrezL2jlu7spA6xq5CJz2O+mVBx64PO8n7to98sgjJz23jtmknxMsYBY1Nx+Hi5lFD6vFzg2xpTPj5zfO9YKq40NLXfC6Jo7BrR7ngck5h7nDrazvjN/a8W59g3+/AdDNFvzwrWP6hZtpD7O+z37cDW2OQdrcqvyAfmXXS75JdwwYz8MxfsjTVpnjUP8xOqv+Y3TsB2tgS+63oo/PPXMD+0WZ64Suv2L6InDa76TXr7s89thju8fe/e4L8SZ9fk/6ghv9nZ0/9uZ37Vs+GPkd6f710fxVjJW8IVY6gN6Mn/04/UnVYdzr6QOKzcJFlSs5v1tRX5nxWzNOf+Jazr/fsFpLfAiv1n1yXvaysoOc362or9yu4/RDjtlXuVn5GT+fu47T0u/vSX/Riz7yGlvXij5E22wh9Y8d29Lp+o6xo73I5HPDOQDzuCi/J/3/+Pb/afdP/um/3G++t37/ub+95Yu/+It3L3nJS/YyvOUtb9n9sl/2y3Zf8iVfsnvNa15z0ntrmDfp50S+GWAx+5bCm5CDRe1Pq96YjPuTadVRnvHzGa/Qlwes3ibARZKd12p+zuk09Znx23u84rMpP2i7tYTtat3r3/a87M1/ZVfnp02OK1/U63OrxwXZA/xMor3Zn09S149j3XfSHVO/5g7IxKOV1Ad18Lsa27KH67Fz7Fa1h/BaoE+ta70vAv/a5/zO3ate9aqDf6CIDThHbtCBN+nveMc75k36ReZGf6r78Tf//DUPmYo3hDqcc/O60OlPnbyB0q83SpVlxtfjnX5S395Ivkm4SLL/tYaWD6+uFq4xxjiHlCHtskZdvWb84o53+h3osS66tUSfHLPOzsP+GDtwHrO+n2JrvNO31n4O5WdSgh32VYZVjC7eofEV6pKvb9I//EUfcTL6FOhtoQ/XWqef+VW27K/XDrLut0I292Mhf2wvypv0G2XepD8DYMGycL35aPlJmRsTuAnqjeCNYn/qKHsueV7HYMbX452+14k2397YB9l/UWQe9PbRdnMDbZhPvq2i9UjyvI7BjF/c8U4/17frGVgXrvlcS6mTY7Y1xnnY177OThiHWd9X2Brv9K2xKKPLZ1pX05Q9lzyvY3BonOuf6zWfw5Bv0v1sBXXN19xrC7nWOl1ZjVV7D7keu+4awM2Su5p3cu5n0s/tzkV6kz6b9HMiFyyLGejjxgQWtwse6k1ax+GYvmmPbzmsnTJ47ejrHppgP1wEWWofc5D8kMi1KLO+7qyWY2t9A32sGQ9Bv1tfwNghzsq++qjn6evQ+oZZ49e2HLUe1Nhaeg0YrzU9ppZwPfXlwAZyvSq7DshT6vU2X3wp2/pDn3TzrDpbY9pLzvk0dsB51v9mybZAvrIlOxfmq+2dAL/dhT9mNL/d5Q7GRc9N4MJGFha3/dzMLPKkjnOjH9NHTFohD28g9Mlh9J66FtYOlBnDXhta+rTBL/20HPZdlDZzsw7AWvFDwrkks77uHD3GYbW+cxx/HPjBFqr/1AHkrfYs7KEbT3/WAw6tb5g1fq0e1HqANfEcXfXlmFp2fUC/eUDtJ3dtiGtfzWP1Jj31qtxBXHIwxgrGzDnR3rGc85a/tFNmHtizlum7WTLtquYrWdL2TmC+k34bcN7fSRduEtjS5ab1YYSeNpJ9h8blmdB3aEyor98NhLRJPfp5QOXDyHHH8ru0t6Jv9aDMeQB2gC02dZ4JY/alLNN3c/sO6SMndX3nuXJ+OEP13+Ha2ZK3OGTvnDg/zfquc0p/cqh+W+Nyu/chS+plv2RNV+OHPqMg9bbocqt9nONv6zvpXd7ZB7n21DFmXZfdPZM6kHmqe4ydpP3NxJoqA+crOaGf+dwp30l/wxvesPukT/qk/Ua98tmf+3m7f/QP/t7J2fkzb9LPCRasC5q2/rSsjB4/lSapA/yUip5wg3Boi27+ZOu45/BM64OsS45TNx6Y4lsA6131Ex+qOY4dMmN8AOnLvur/PPuAuK6NXCPoc2RdtMlxbfRDrZA5QNlzmL6b0werdd3pQl0vuVbquhF9eeSa4ADtoJNv1N55ssHxvoL0Z+v6hZwTpL/TrPHUuRP78hlInwdQo1VNs47KjKdffRk79eyrbeon+ko8zw1/zke6vFfrI2MoV71D9jVPdFm/h+yyBgl2N6OFjJ1zWcmCD/pybrc7/LaXt7/97fsfGupxMzfoMJv0cyIXLAuYN0FSb1RuXmCx8yCB1KGfc/zkzUUfDykeAvoAxvTFja9PHmLPpL6srVi32u/DRz9ZQ9rU4RD0ecBCjmcekuNyln0ps978ULB1LOeffeI4865rS27kukzfjfXl9RP1unULuTagyvrv7GlrTG1Y+ylnn1yPPaQNOh7Qre+k+ofU0Y7cujXe5Xyn9nVrB9BJVnWU6tdzf8DCPnVss/7VfmtNAtdYtAPHocu7rg/k9A+pU9dStefIOla27NB33sg5Z/SEfvPUjnHiXq8e44eeHatxZUBO38PZMV93WXCj/+nlh37irVc/SIQFbV/KwkIXbp6Ozq4jfYk3rO2d3MdD6lCNAF0eLjwksbWvoo5yXoPMIbFfff5TZ73+Z9UHziX7TsOxa0uIt3UNpu/s+7bWtTZJXbeH5Mox68n8JPO4XvucJ+fH+OkwF/2fdo0/U8hr1q2xeg1uRh0zp6SulU/7xJftv+7ykpe8+Jp8yHH1zJZcH8roYpdxIHWl9lUfK3l1H2u/IvOUG+mDVX/WoRvvePmLPuBEOj0X6esuF4l5k35OdG+37Us54WbwgPqTOS03jXZbPwGnr/SZ7Z3cZ42yLp0MPkAFex6iPKT0zwNe8hqAOhX9qG9L7LPuy7nQ17G1XvTLW69OJ2Vxzjn/6TvfPq/t6nrkugWuqWzJ6NfDsdV6EnWTG7Hn/DTrGr2uHoCv9M99fMwafybISa6brj7gNaAPeVVHqZ9f0H2m2XLkmNeuPotBHcYk1wfj5Cir9ZM+bdNO8Od4kvbQ+agyOuTS1Ycx51tbfafOaftO4zPzzrFOBtvhbJlN+jnR3XySsqCrjbL/mRA454ZIW2707mFQ/fAwEPru5LajqxEoU9N6TaytfjnnIVSvAaBTa5526md7ln3A5iPHJPPZWi/Oi6PTgdR3rjDtzWkr9XpArluvZ67blQzY4MvnhfaJOrRVFvzi43rtk25dVzvn0a1P5Hz+eT926xqeSbJ1grpurDuo7zltHYPqN583qz6uG61UfcjcxPh8RkpeZ3Bd2Cb4MoZyrln9O6Y9vtKmk42Hj04W5sXLOjA+2O+8u/lfb9+xPmsdHFvJzMu5DGfLtat6ODNYsCzc1Y1cZXDhc2P45tabhDFuiArjxOEBkLqiXcZB9mEDd1I/sv1Q66NsC50doG9NGeOabr1lkpQT/Z91S455jWmVIfOp9QDXiFSdTl+Iw5i5GHP6z74f2X6uRXc9IMfQ9/quZDYHxrEPMqYyZDzlVbzT2JsHuvYde78Rzxy6sQq6qzX+TJAh6wT0O2bN7OPorg/Hyi966vh5Zh94bdRXF7ZyA3MgttTrrH83vLC1hrbWGvb0VRsgL+cHqW/slDu0qeSckfEjtSZwTJ9y1QN167WGzgcgW7vh7JnvpC84i++k5w19DLnwT4s3kz64YXhweOPnzfZMgA8N6m89mH+tb1cT7aqcfjoYrzUH9Fc+z0PuqPMG59GNSepU/ZzrqibD+VCv/WrN1f4tuvWwuq7odGu9cj322mT+nZ9DORyTH+S8n2lyQn9dV6s1pm7tA/1S/+qLsWOvS9LFE8ZW30kHxnOu5gm1BsDmFB8rPfOv/x4IrmduK8yb1rkT0zrav7peK7nLueo6X2twyIegP99JP3vmTfo54aJmweex9ZaDG8YbI8mfajk6Pf0DY8TPG+lQ7NtVri1jYP3FfqFG9OUBaYesX1E343HUmnudoPqUs5RrXpm3udCK+tC9NYHUSbnONWsx8tnJtWUM6rVfrbnug3TrWhMnx+iruXHk9TcmbcrH2lcYhxw/rQ9gI9G9GTU30d8zSc7rbF2AegI61E+6Ote+jAHVnjFira5Zty7tg2qnHnMRx52TOimbJ0cXUx/q1FqZR30rzljtS/8cp5EBGYjJWsa/+dgvx8qZH9TrlDB/WPmouXN/DmfPvElfcB6/3UW8CbkJOpnF7o2RcqXqreJViOMNeLvL4DkPxVW9s1bVttaOB0+eowNpB6t+cAwY16dvYLrf1nKjciVz4OGujnOmHuaubl1Tp1lf+Eh/I9+YDJ7TgmPddVcH0kdFvdW1Bs8zLzCXXA8ZV7bsK/o7tNa2fED6qXGTGmsVV393St+hutS6bj1bKjUGthnvGMwp/di38sN49ya9m59+qwy1PknmgHw9c7oe8pmdZD6rz4KVnHiNmHsdJ0b2dz66uc2b9LNn3qSfEyx+FjQLmQWeC5qbyxu9ypAPD2X1Ur/qHfPmCLSH210Gz6l39/YCso6wekuDTZ4DNjUm8BDlQZaxaEEb7XzA6TvfumS8G5ET8sgc0DFHwC4xz+yvcvpwnok+YOQr3IgMnmc/te+uOzoc9e1fvV76qtdXe8+T9AsZ3zHuhS17jkP3J6TvZHW/VT/mAIdy6+JWf3dKX1Lr4rXFBmj147njnQzGoK/Gg9WbZcnrg4w++UHVtyVvMVfBhwdkTsbw4PkMq7w4aj6p29kBdrXOx8r5Pe+sHTocyMzDa31ITuyHHKffmId8ZK62w9kzm/RzggXL4gZvhnpDc+OJfSx2Fr8L3xsydbCzPw8wFqziKsPt3lZ4kGQNePjWGkHqZX/VA2J1NayxVvXmevmAq76hxpfTysST7E9yzuqYZ7f2UpbVPJVh2rNtgWuR936CntfgmHXZXWPRf42xumfAMXyv7GGVG7rdWktWtpB+Kl1u3fzTNv1hB/ksuR37OJKsS9Y2nwWJ49DJGceauuZgdf1yXWoPW9dbHTaykp+njuMz51OvdeZmX5cXMrEYM0/o8lvZQc7pGJnrB9mHz/ocOEYW8so61HHjbPkQ8vKFk3bD2TKb9HMiF7oLPBcxMgvbG7n2KQM3ZNUB+9EHY3HzcROu4gJj2KMn+PLByrg380XUA/SQaRN8oIettep00eMgjmOppwy1hthBxtKfD1bI65WYx1m33Twkc00dME/6OlmcIzAmyo4Bvk97XUev10Mnr4t9ypDXA7/Y4g+Zo1uX2PshS/zqlzbRV+qKMY/xUXNDx5xgZZt2yrawFZMDMlbKoq76gP/Ugdupr7tekPO0rfUA9br6O5aw1nJzKtUO0LG/5lj1tVGHMTFnxjjwBfVa+4ZaH+pBxsjczTHHlbv5SNrJsTJHXgfH8bl1XVf3sTKkj8S4xjrmmQDoUYPh7JnvpC84r++ks8izPxe8N0aHelXHfm6Qzq/6Na6kXuYC9m2NJbeqD5i/D8eUodps6a7Ax6qGoH/0YKveNT56+S/3tT2mr/rJN0viWLfm+IDp5tNh7umrmyd65JdxwL6tsWT6ru1DhqojjifVdrUuJX3n2qDfdVvzWPXD1vqquSXpo/NfbVJftOvkVQ3wU8fTN3GNb//t0Aeen7Yu2KnXxUp55aOSdon9GQ+29A99J30Vo6PmX+8XbLs51vyOsbPvmHW5hbH1RQ72rehqsorf+cpYgt58J/3smTfp5wQLuFvstZ9F7k/ijHNwg9cbA716Y4F9nV/HuriSesoc5EQeSY7LrejLc/uYnyDX8WN1Pbwmnm/VENQDdHk7mW9sOKxnjY9P+zLOMX3iuHlkPo5Jzo1+c6OV7g0KpC9zSN/5RiXzuMjrCS5y32q8rtG8ZuIY0J//FqJjtTYg1xvot/Yfs74gc6u559gqrmCj/squyjUv5W7c+QB9ub4BHeRc+xdFT11Q3qrLoWcWfemXNu9tayf6oE3SLse6HCFjgjb4kIyr/iqG1zRlyPyx8dz1CXWOYDxIO+RqV/ukjtOu5MS46Ws1R+XqE4xfqfZgLHOhtYbD2TKb9HOCBZsLmBuBhe4iT7gx8gbjp1n1tKVdyUA8HiSJOjVu56faZk76SL1b1Qc1Z+bGQQ3Q36qd4ytdfTp/+sEY0vlWTr28rsrGtoUup0N9nR8wH+aCvrZS5wZ5remva1I5fR3rGy7qerrofZDXM6m1rjWmP23rtQLHqw/PQZ95vbUj37oOtnzUvNSpuTtXfde4+oA65lw58v7p7iVjQs5T6CO3fCbTZ3x9IOccAJvkVugxnvVa1SOP9KWc+nl9wPiMoUOcRB+ZB3J+HWaVo2ijjmP5Xw7r/QFZm8ybfn5gxVfqZExkz1c6NS/kmnvaoQPZ183XcejkVcz0Yc7odLIop61+aSHtjUPeYF/6HM6O+brLghv9Ty8/9uZ37R8Ifj0B8iaoqMuDA1j43ASnWfj6r7ar/mSVG3nxIGTcm5EWbkVfNy+o+lvzTN1jrlHVWfnmQZnXUPLaZj2TzEkO9SHXsVV9jkHfgG3Ne1UD5WPi5fzNv5vT9F1pr+d66iupttU3rPxvXfua51aOXV6QNupUv7DKt+Znf/WlXMl1fixbNpkPOa/8npce47V2ifXoaiF1frWWK9vVmPZJ6hEvN9yO5dyl2n3yx750/3WXD3/RR5z0Pp3Mv6PGsXY1VqdT6WJoyw9Qq7pWtEE35VUt6e/y7uh8r+a18oVdXjPsPuZlH3xydnrm6y49T//RczgT+CmUBexirwudG2r1k6qkLTeAPy2v5GQVd+VTurwcz/ZW9AEPuRwDcnUusjXPtM+3Cukz2XrzkL67awj0+1DOeib01f7ah988r/qwmkte107mgWs8bXPeqxqA8pZ/Wsj5Zzt9T++D1XrfqrXrcfVsQA9yrajT+cvnGKRd9VVtWVdinMyrxq35ruKmTq7N7E+9apNo71y63CvVJmGM+525uKnSZ8rU1eurrxvVy5yQAbvuGVhJnzk/jtTvbMWx9MWR8ZUT4nXr1TyA/vQPzFnq9TKHfLat+G//66/d/fd//k/vvvd7/vH+3HonmQts1bfimqjXqOZlzrR5DVLWpotpTll7a5CYT/oW5cyt+kFmLplD+hjOjvVTaLghWLAuchZxvWnUSfKmUObABl1uppWcaJdxs7/6BM5XeYl+blVL3jwYVrV0Llvz7KBOPGzSJ22CL/W2fDt2Gnjw1TlVWTiv19XW2Mestyqv6pNz0bc1SBm2/HfU/Ke9tqWuW+tdqsy1RDfl9FGvn/0r3+jWwzV2aA3UdUWc7K9xUz9jGYMj7xdxLDnNfWWczKWr/com+8W5mFetDf2pcxZ63QFsOlfzUQb9gHV3jvQfW1N0iSn4dQ4pC3ZsGms/4KvWOXMUbc0FjJX5pQzM6b967Vfv/ts/85rdN/z1r9v7zlol5pLrEZ2cU/WfaMPR1RLwBfSpCykzVuuY4/qAqpek7zovMEdIP15b+8gH2+HsmU36OcGCZYEDi7jeNJA3gzcprbL2qbeSJf1k3OqbG7LaHsoLtKUV50qLHrbnoUcfctbSNx4cYs7q5xg4Tgur66OO+jy4GdPukO8qr8b1K6tcqFO+jcl+fcLWeqOm6Fc56XKsvjlP2Vqs/Buj+sv8BbubsZ4uuh59yNdzLWmVofogTl0neS9Vf+ibE2Bb3wyubEH72g85J1E/80SGzFsd9c0P6vw6WXtIfXOxJnDIJvsr+ODoagPm79j16jmedQDyRKerAaQs2Lhxdjxl6GTrYExz/P+39y7Atq1VfefCRy4U2rwkYgt6EaIo8hBbEYw2YCCIhrQICEZtDXYJ0hqDL6BbA7EKsMpHKh3whdIJbXio2NomShQk2gaqbZSoJHa1vBQt30B8otj2/a27f4f/HXd8c6197j6wuGf8qmbNMb9vvOf3zT33OnvvI1mT+SqvqHHVZf2JNWedGWuVa/q41TUfcKN9Zz3min5+A4JuxoGV7db67Pbfyr7GdJ4zaF97D6mbfsnHT9clc8x43tscy1qGi+OGO3m4MFiwLGRxw7ColXOTQC7yai9sprrBVn4YcyPlQ6Xzfd68MsaVHCOvHIPsJQ/MVQ/Qd6ybT7J+ZEgdc/FIf1u+U96aT98cXS7Wrw4w7otSUn1wkKN+lLf6J51v46fc+TfnLd/oOJZ2V+NY3ifuDf8E/7fu8kG7Bz3g45b3kmfCs5751N21d7r17lPu/RG733rrr+99C/quhbqucg5fUH3nfVNHzEd/aev1IXvjo1v1gbGMAcrqwCH/VYa0B8ad46y/HO9sgHH8k3/Wwhk41xy7/l6O3qH7JKteKJt/xRphZasO8YUcfdE3R8Y4Ml/Q3jnOCfPqeCa21JrR0Ye2Xa7p48/e+a5LflJHkBnPWFkXGAuqbZejOTmHH3Trc1377I+y86KuvYdDukJO6ErWU8l1Rw3DxTMv6VcIFmwudDcMY8h1kwAbATs2bW4KN9eWLXR+0i7HO7byyqOOyUWPAfnXfpgndTG+ylm2akqqX456P7wXjq18p522h+b1zYOvyyXnwfE8kvQBqZM256nBHDiv8qmypO886phcbWOQa4vjV//TL+/Hf/O6F2++0e56/exv+obdi174vXv5Ez/5U/d/L1o9YS3kp6KuCXCuWyfqg2NS7z+krazsJWNA6rsGaxwwVt2jlaw5Ze216+oR51b7wfFVLamTdP1N/3JIr5sH8+MMqdfJntFPW+0l9VI2J3PIXDIeKKe+cZzL+F0uvMhKXYfA2kh7X3z1gV768JN0MbetNZZ1ZY5pg7wC+27/eXSxt/roob8kdVc1UQNgv+q/ctaeOQ0Xx42fRsOFsFqwbgjObBA2CjIHix47Fj64GSD9VdstP2lX/Xd0/oAHlxtTHEPfPC96bJVv5rbKGbyu88bKesB5yH4hdzl1vrs+O9fNmwtU3xyr+eSYeqTqMn+oBq4zBzk2H/1yQJevY3n/r7ax7CfzvDQI49lreveKl//Y7rue+2376w+/80fsvv25L7iRXoKN96CyNW6O2HOs8lVHtGVtpW3qQOohc6Cjf8/VPnW8XvnnUN6qh5e21VyNAzkO1pHnqpOs8uGcWEPXZzBe+gBiJ/YBDsna5pww5njKsMoRHfPUpuo6B5l7lwu+JPtrD1b2HPY8feQn6eajn9X9g1W+2GQeyF1fAB91XtuMnfnbK2tJv3VMO47OLzguWzJ+wPjkMlw885J+hcgFy8J3s6TMBmGxI4MbKHFj1Lm0rX5A3bSrPiDzUeaLVP54DBgDav5dLhcxxsY/Jl8e8ukn9ZiDOu81dP6gxs6fGUyq76rT+c35zKX6htW8fjlv1VPlqtv1r+YImQPru96fQzGSLl/HMperaaz2k3FeGqT28D+9/j/u/vGTv2QvX3PNLXc/9GP/fu+nQix7DMj5BTznV7I5inLN13HszLfauo8q6hFP1Ev9jNE9I3K+1qHsJ6qirK+tOVmNU4f/auG56mROUHuk3NWQuls+8nll/PSjnOuKa2Du0B7v7GWVIzjnWJc3mHfmkXVAfgqeeVS7rhbjrj5JR9d+pB1YO2flVSzOHlD7kr4g90faQepmH7t+d2Pa114Ac6uedXJS7+Fwcdx4dw0XAg9nFjIbAnIBp8yid7PwcHAzgXMcdQ7SNvXYRJJ2btCUoeaGHzZdxRg+RIFrzyl7viljmcNWvuphU3uePjIOKFd/+UkaIGc+2UfRd9dvMJfOFjr7hLq4r51fYAx7qPXISjf753jNwzkOxtLumHzyPoj+3lPr6dTHao+4B/lJ+rv+8t33g37/oyf+g907z/r+/Be+bHeHO9xxLwN63X0B5NVLKlQ5c3QdIjueOIZd1pN2jJub9Yh+qT2fY+o5DzUG1HnpauoOUM6cfa7UPOp4Use45ujuCdSYsKqhm4e0z+fYKi6yPURna27L3nnOssoRmHMekM3dvMGcuvsM2EjqpB2y3yxVjCt8U0x8fq/jGU//qt1j//5n7D753nfZPflLH7///RDyOtSHzJfr7EvWXe2BOW23vpYAY+lP2eep85D+md9aG8Y/RhZ85H4dLo55Sb9CsOjzCyGbg0XMA8HNBG4Qzix89Rljk0qdy83V6TGX19LJNbck81Omrsz/Spw7jsk36z2mlrwfHlD7VPNyvutNtQX86mNly7m7z1Dvo5+2cNgL9K0n+9PJqdtR88g1hk21yzq3YmStyu+J9XTq5w7uQX6S/gEfeMtLfXryl37+7s1vfvNefta3PG/3aZ/+3+5l5z3nfemOQ+sEOXFdZP71fh5jB7m+0p5z6jMGyqxF/NcYaQ/W0NUl6bOSOShD6tdxdPUJ5gLGVr+rIWM6n/mnvtc5Vu19TkDGTZ+J47VPcMje+exDp8d47RXn7KUvmthV2zzz7JDVMyrtJeOmj//qNrfZ/esXPn/34Afcc/97Hv/59b+0e9vb3rb7qZf/2P7PNLLvQP+1PseT7Is5dvbVLvsBXf/Tp2DHvOhb/8wjr3zLMbJ9hPQ3XBw3fjINF0Iueg4WM2NskIS51Xe+nS7kZljpqQvIbGg2bpU5utxWmw9Z3+jgh4dEPhSw8wGi/0N6oB5n43MGc13lm6Cj3/QFtZbOh/bkkr0S84CuN/Uwl+qr2ko3D/rCh3nbC77Q5KdFjG3J6GJTe8RZMg/tgfuYuuh5rPLRPzAvyMYRe8VZn9R8EevslPS4Vq8DvfwknZ5i823XvSz8zKt+cj/2+C98wu4xn/dFN3jR0C8xPQB/xHKes/d2JXfgz7qg3s8tO3NJudqLOj4fQf/kaC3Kzou63b6oNtWnZJ6Zr/4gx0XZOXxql2M1HjDf2Unex85H2mvnGEf1qQ9wvH7yvGUPOd/dL6hxJGV9YKM+Z2Xm1APWoWSczjZlMG76eNlLv3/3T57+VfsfH2NvPe/5L9p99VOfubv22mv38+y7x33OQ/cyvvCx9Ry1HshegPa1P9oCtuTH80JfaVd9gvPGrfteqm/3NHoc1aZbd0As/QwXzy3+ev4f1pab+l/U/sobfn//sKobSFjkLOrcTCz6lY36zq900y9kDOagyh3OAzo1HvP6SX9yU8YqtZ5DdePTsQpzXe86e0k/q1y27p2kH2McY9eBr5rneen6A6saE21X85Vae7ee0lfV59pzcnMZE3uPDjzlyV+y+zc/+oN7+c2//Se7H/6hl176OfRPf9BDd//qxf/7Xs7+09u8f+nPuMfeN8BGP6DMF2btV+u4s+30VvbW0tl1PbROQaeOAeOZf/V1TM4dqzo6MuZ546VtraP6OuQ3fbk2s2f6XOWUMbXr+lDjHOoV+taWtmAcxh94v7vtXvqjr9z/VSN9Vf2O9MGfOZU73vFDdy/5kVfs7nKXa/fxeQlH9797+KfuP1mHH/mJn9t93D3vcwMflWN6n6SP2k/nuEZ2PGF8FUf76heq70radPP6Yu7ud771Xr4cbuo7182V+ST9CpGfRGx9ByqMc+0DaaXvPHL3Hbx6kjKbyQ3FmQdQtefsvAdjNTdtk7SRY8bwxYOgnp23Bq55AB1TN6CfvjiyFtiyT2oukH6U9ce5Yg76ylw6u9UnIICPbv6YMc/mUntEjyVrTNCD1XyNqW8OxrRTD9KXuuTmvKQveV8by54rAz0QepOfpL/xjW/aPfUpT9rL/CWX5z7/X+/3Qvbf3krKYPzsdZL3jSPvjSDjR3tjHvs8qnG17/JxLdZPdiF7h8zRrTvwOsfxZ57pB2rOXW2dfKwumDPUeNnbtJHMN+sAfTF37F7OXDjjr/rMON28ML66Xxln9SznDOjpI221B/ogGU+97NNqraQPPkF/4Uv/7f4FHcgPyOnp/+Q5exle/P3ftz9nrtV/1/usMWXQDrKf4Bw5E0PSD2zdY6h+IeNyzjogbeq8OuSQeQ0Xx7ykXyFy87FpcqEr5yJPGVb6nj1WemwYNpN64GY+lFd9iOgHjMnDK/XR4cxD5Jgx/QN5+FDHp2fmzd/4zJmDKKeepC/odDp7ayd3xswdOXsrKesv69SXMKYfqXbmnmNJN3/MWN4DqD3iuqsR0Elb9LIu6fLQNv2mHmPq6HOVe7emTn3MHkDWVXuQvcmfSf/Cxz7i0i+Kfu8Lf3hvY8+AM/dDVvcwY1QyF8i8DvnjOI+t93o1zpl8cq5ivvYg88+eE18dxwX99EO8eqgnnawe50O65OAaMcaqv2lj3rVuUE9/gN7KL7aZBzgm6dNYjkEXs8aBLha5odv5y1pBe8457ks0pG/JPtWeeZ0+HvXYf7C7x8fe4+zq+j0k973fJ51Ju90vve61l3pqXZ3/2vtD9XKs7hfUGOroJ23QOeS36iDTD7/BQNdDag6cmc+6hovjxqt6uBDqgmURs0HYKHXRs8HdKOB8p9/pVj3miM9mAm3gmLwOffqinrbqeM74dSxf7rGvOKb/Wq+Ys2dAp9PVF6x6XefB3LfkGjN9WSdoo36OQWeHbjeWaOc906YbA2PqT7QB9PmmiXtlbRyZt+jPec5S8wD1E3S4j11fwHnHM+b7wthqzVc5r7Hl4BfZ5HFf8IQzabf/H0Yl7YwD5gH4qveyyoI/95V5MZ/+5HKeR8aErXFgzPEqi3HE67ruJOXOFlbPiayt1omNz6ItXci6gTh1DPQNmTfknDJxMm/O9VPt7hmHXo5B9bmqhyP7pa+UoasPqj8wh1Vegp10vsEcqwzI6eP3fvd39vuVXMCYwHq6573uu5d/661v2euRX9aV/pk75l+AIOOkv46MAemv67mk3y0d/GX8uhfAmPpgzp4NF8u8pF8hugXLwmcT5GIHx4FFz6aATr/qMlf16iZOmzoH1Z5r8mcTVl10csOiq06eV2N5QPrTp2P0IXOvcfPTd6m6+kq71LHXkvPmCCsZOn/W2PWRh73zYp7qalfHpKurrrk6ljFT1lfmLl1vme/qyj7gU798MUubjlXfhXnH8/y+MJYH5L2rvRd1eWmQr/iqr9nd737328v8Att3Pvdbb2BnjO7eQHcvod438H54re9K3jftj7HVZms87RyHGo+jk10z2Y+uN9owXmsAxuxz1lbr3LpOOeuSbgxd84G6f3JeOb8h5Dr1xVyAmPrPscwFfb9p7+pRR3vo5PRpvtWea/WsN+2d046cpO6hjKGcOo6ljzv+zQ+9UUzyAPS05y++oJc5VVbjUOs1jj6Tro6Uycl7JDX/zu8xOpD31tiwdc+Hi+OGq3q4MFiwLHgXtDDGZsjFDm4O7Fj8wnjdOKmLzCb1QeLG7eKquzUPzPlQVle/sLUZ9VvPkLGrP2LbF8fsg3l1cfFj7h6QutUudbLXkn6gy5sz1JjpD506hu5WX9HVDj2/EWEMufZItME/ch3r7rtjYOzE2ojJ+vJav7UuDjAvrv2GpLOppI8tsr5TPsPWmpfsizr64KVBWA//8qUv393udrfbX/Mn4V79H35uL6vPueuzvc17mTJkTqBOzd9You/85Br0W9ee+un72PFVvisZH/YD2f0E3fpP24yT/TSfKsPWtXK3Jqqsfv3XAOvIvCF1jVfzTtCxz9nX2vuEeY+8luqnylkjZK9B3Zwn/xzP3gDjYq2rGPqr8+nDT9LBGPYVvQ+85vpfjOSXS9HLmo6VBf/GAOJsfW2QribRpwc+qg4co5OgBxkb6An31vNw8cxL+hXChxLUTcdGdLHnnIs90Sbteci7wYDNlZuHze5c2kPqVr/K2kL6Vc7Y1bbWDepk3ZD+wNzc8PoBY9a4KdMXUM9+dnaOi+Ocq7/aX+XU7+5dxk0Y2+qDdmmrnLmkTsrZO2Tq6O579bVCPX1mLGBcn5C9wBaqDaTdeWRts85THEfOHkP2G/26DiH185N0dHnJ/Off9f1nI7vdV37ZF+5jZeyUAbnmU2XvT81llb/+qm/suQbn6vOu21f6gDpe9dEz1+xhyhxQ5STjdPpQryFrPiSbe5JxoZP1gy7xrU0yb/NTF3JcMj9A3w9j8Ge8mkPaKa/qwp9+Uu5q7HJUl1pzHVcfjpO7mBM+M0auC0lf6cNviq/Len8GYmPL+a2/8Zb92Efd/aNv4BN//H11/krMve5+x/2Zg7+vrp4xV700Tua2qqOrCapP5m+KTuZpvNQlZ7/xzbyHi+PGO224ELqNBsgudI7ukxJwY0C1VydhA7Fx8cn8yh7cZNWvPgS99KucGxeqH+lk/NQj4dqNT7z6oOCs3qp3gF6O1XxX41L9ES97sYqfea5k6PwJD8/UhRxL/U531Rdtsk7GtvosWzEZv5xeqCs3V9ke572mB+jkGgP1pH6Sjh3/cdGX/A9fsR/7vd/7nf1/sFJjE+P9d3+x1/+Bl/yrSy8OH3OXD96fGQPj5X3hnNT8YVUrtl6j67pIu7qvIH3Alr5zxnKtVd1cpxyr2vQnKztlyHy35Hp/hZjZ063+Ejd9mTM2XU3Q1QDpV/RnbM+1FslcOrQHZevzDOZV88cG/8SpvrxOv1JzQgffNV/9ZE7ym7/x6/vzX+3+xv6c/NF/ecfuN996/fyH3PFDL/nEnv30gu/+Z7tf/rXf2/2/v/HH+z+X+sQnPnH/51Kf/U3fcKn/xN36ugWZm7lmHV1N9hJyznHOl6MjGVtd0c77Olws85J+hcgHEmc2Wn0gAAs/dRI3SdpWHcEP+rl50l47N1nNCbnzwdjqExEeNvrWTz3XGGIefDFZUeMp+5BgPv0n5pVkP5Ic73KV2h+uqz7nLmdQtu7qT7LurLXaw0p3VQfXHpI+oPrjUIZVTHzmveC68wvKaXOMXM/ntX9Py2LP7CFzOS/1XvyXd7zjTLr+ZQAbXtaf8vXfuPvYe957P+7Pp9eYvGjw6d4LX/Cd+5cHXhx4geA/aXn613z57l9827MufYoqyvXeo5cv3BxZp3GVvXZdQI4njjtnzFoPOGcfyYG9kPZSe+nzCtKPcrenoJPxc57738Wz91zn+sDOA1JOMs+Vb8m89aVu2tkD9S6nLuWEXLtPXFf3BLpx5zxTp5g7aMt5la+5pA/20rc85xtv4Eu+53nfdibtdp/1yM+9wXr5/C/473eves3rL+0RfD75a75p/6Np/+fPvHI/Ru8A/a6XiblZZ9ZRa5K8x0n2+7w6XZ7O572C9DFcHPOfGS24qX9Y/9fe+ic32ggs6GPGKrlRgWs2D5tiy5aHyB/98Z9e2jzaAHbV77Hol4cupJ9aT72uOUHmdaguY4HxUj7kK+PXGOnrGGptSfYo5S7GKid1hbmtHPGTX3Cg60fKXR6ZZ2WV31Zuq15A2hwrp/+8PjV5Rd5v6O4FoPc1X/GE3Q/+wIv317xgo0MM+IM/+L3dgx94z92f/emf7q9f9LJ/t/v4e3/Cpd4CPuqa4IvuJ93ro3a3vvWtdv/HT/38je6L/pOamzrmc2htwaG663y1l1rTSg+yLqi5Jqt8a3+g1t/JcJ54HbUnXW+NWUmdlZ9K55ex89QF6SfBrs51vtCpOUO1RYe1zH9m9F/f+SPORq/nUM344l+bPuADb7m79k43/E94+JeqL/qHT9zd+c4fub/mm13+J1Lgm+Mff8Wr92twq0540pc+bvezr/qp3U+86rWX8qs9yPpX/uCYtZA63Xiu5S0dsIYuJ+d4lmDDNyecP/5uH7IfvxzmPzPqufG3i8OFwAZi0Se52FnkfCeqnDjHmQNffhcubtTUqzIPEfVA2Tw41w3Y+aly/S4f0mdSr7UF5/LTlMzXmNlH9DzyWrp6zRsyfq2t+2TDudRTrrpJ9ijlmi+scvK+o+966uwFP8576Be6PhsPujwzB22Zz345nnKy6gWs7LfkJK9PTRb7Zc15v6HeC/XZv/l30uk343KHO9xx963//HvPrq7/+XTQBxALruv8pdz4YsqLxu/87u/ur/F56N4n6NRn0rH1bOllX7qYqZf5JakHWZdkjFWNkLbVD/rarGTZime++YxzLOOKsvMc6XNVz8rPlg3XjqUsKx/qZR3K6HSkL+0zZ2PoS/Kbtfr1dqtmY/CvTemDH1GBF3zP/7J78APuuXvkwx+4++R73+XSCzr/2dE3ftO37G300WG+r/2/fm5394++x/5l37w7O3Or/Ur50P6BrLkb5/oYHcg+AeOpzxw2vNSnz+FimZf0KwQLloULubiVwUXtRujmIH1Bbp6qJ8jq5cFDsuayygs6n5C+0ieszmIuytbmuP6AmMybX/rioZxjac8DEhmyBqjjXPMCy0NQf8aD2gPJnFIW80m55izO+8+lYO0pH4pZx/BpP2qfIeuBnMNH5qBvyPGsqcaX9JsyHLKvPTvlM0etBbo+b61TZObzfxzNL9LaPOKzH7n/8RXw59Nrf5HzZ2zxwX9vfu1d776/5ossuaYN1+h5j6HWU9fToXpAXQ9IPcbwc6iHNb+VHmQsZY7qo6PaZm6ytX6158h42oBj2jomxrW3HN1zAntfmDo6P5lT5XLqAnUh68g8O19db2sMxwQb6WrQb9Zcnyfp41Mf8sj9f/l/7bXX/4+j7BP+3CLwF11e+iOv2P03n/TA/bXoJ88c//n1v7y3/duf/pBLOTjX1Q+1X5K15wGpB1vjzh3S6e49ZB6iDvUNF8+8pF8h3JCSmyEXuotd3ZzDB5u7bojc4OqkrrJow8bjQdblAqvYXR6AL74o5MuDm5mY2Jln3fDksiJzJKY+MgZjqZc+HUcHew8wvvU4jg2y/iBzWPWj09+qteacepzNwxjCmGzFhPzEHLIfYLzag8yDo+YAxuv8S82p+q1y/YRolT+gT06chTzpMWd8Yvve0oOuF8w5L3lfnM+D+fpJunOgDv9d+Yef/VM6P1P7Qy954d4nB/kqAzavefXP7F/o/87DPusG+WWNxqqkfqWrh97UvM2L3jnuHOT9hoypXrWBTq/2wLjQ+ej0U67POsZX+Vbb7GnaMIYOdDVA9tbr7C2kvhg77dJPjZNcTl2SddQ8IX15PzLeKoY+zJ/7IfqpdL3LOPjgR8U4+F9FP+6e99n/fPm3P/cFu6/4x0/bPetbnnfdy/krdz//y2/c3ee+1/9nRlmLcp6p+V98+7P3n7z/j9f5OKaX2aeVLFt92RrPHjmvTrLKt/MpqT9cHPMz6Qsu4mfSITcAGyR/5strFzeb0Tk2AOSGYL7bCHWToctYtVnlUvPK2DWPQ+ArH5xbZG7KXY68tNW+GePYHPXV9aJy3n6kvvNJF6vTg1WMyiqm9lv9rD1I/cpWDpVDfdjimDjZl+r/FMaQpa6h7H3qSTfPGH8H/T/87E/v/TzxyV+9H897S2zOfLH8X5//vP35sx756N3d7v4xe91Euy/7h4/ZvfInf3z3mte9af8jM/qRLj/JPKFbZ1L7Um0dR6/z4zi1HxN3pVPp4sJKP0lbccz4ec/zWZi5ijbdM85aOjviM75VQ61nK361Sd2sK+uWzq+ov6oBVnkd6h2g1/1Muv05RI2T8KJb5/Cpb/PPnjGG3dO+9it3L3rh9+5f9B9x3X7s0D5J/5Ay1Pvl3E0d7+47qOe6hM6nY/Mz6RfPvKQvuKkL5lfe8Pv7By/fkSZuTDdDblQ2d9WX1KsbqW5kYfwYn9imvAV6qy8Eypz9opPnzMN4le5hkbqO8zJS9ZLMU52uxk4POt0tqj75re6//WFupVfp8lzl6Dgc2wNhvMsp40MnY1v9p6+VvKKLmTadj1Maq73w+tjeAWPsYagvDNqmP18s8JE56fsbn/6PLr08fM7nPvaS7nnQF+TzhfF6jyqrGiVrSbI/SfYPOp3aC+l0oep3titqfcfaZi61luxJ199VHaI/QLf66OxXfT1UV+c/OTSfrO4ZOeT5gfe72/4l/a53vfYGuthn3zq51geOQY5DzkHO69dfMuVT+K/++v/50h5Dt6v9POsLjLnK5bzjcOx7gqzG7n7nG/4C7nmYl/Se/t+HhpsMm7Vb9CzqXNjIbBA2L5uZDcti51BWz4PvWusceJ3j5FB9if6qLBlHH+ADDlLmu21qsXbPjNdeGM/ajZ3+RF11yAU9r4/JE4x1SA8yHnQxOEvV56Hb3U+wL4yl3PlX1i4xZrcezKWzoQ+dPgdj5gRdfPSoTzKGfiB9dfJqvStD+tYe9OE1nNIYZC9AGV1Juerjl2v8cjivDrbI3gt1OdecuOf8LWde0L/syU+5wQv6am2nnOSexb96YMyVLTar9QfY6z/jgLZbz4uqw0Gc7IU4v6Vfbc/zHGA8n32dvminLShnjVt1eNR6wLyh+qg2kDEhfcGxz7fzznMGzpmn8+bgmbwla9Jeqmy96HEgg2fGwLqNZx7dPD1hj/GC/pCHfubuK5/yP13aY5I1AX5y7ND6AuNVzjue97zej6Szr2PY2LvhYpmX9CuEDwDIxd/JbGQfHPnPSj5YVvp1LmPmOKx8bclsXO1Amc1JLPJ1s7phsVH2XOliIFdf6vHgSlIHtvLc0uOhqo56mVvKqxhV11ztwyovzxzYQqcLaadtkrllDupXm5U+dPpdfHzUNQDZhxxfyV2dkDEzjqQPOZUxe5DrQjlr6epKfUgZnE87/qWqUnP6l9/3Pfu/jf53/u5n7572Dd90g5eH1doG5cxD/cwr75fj1dbcV88vc8a/L7c1To6pz5FUu06HOWNv6VdbdcVnCKRPjrQTbWtPcg+mH3CdeE46+62+QZdX2lhzravGYD57kf6NvZqXbp5YkHrAPH6zLtaSZH5AvwA/9VjdR2Mgg7VnzMwz8/nZn/n3+z3GX0767u/73/ZjibGTOlbz6mJdhAx5z+W88ew5NWTew8Vxw1U9XBh+qsxChm7jAbIblU0DXnOA+lzXF0uupYuRutDpwErGzi8Q+mGDokO+uXEruZlThi7GSq/GSVlqnukvSR0e8KuYcqgXtf/eQ+lsEh5ymfOWnHnWuvRLDl1dl6uPnjnkOOf8lJA6mIeuD6BO57urmwPd9Jc+OE5RBnIGalitkZQ7W1Cu82mXz5rMQ/kXfv7V+0/3eHngx1y43/ZWau9ThswJGHdO2Ry2bJHT1mttE/JTL0n7uqZkpcNhHPMyDsdqfSVZH/eh8wnVPnOqPfF+Ajrdmsn9VmOmPWQsoC5yhpqXoO99YO5QDNAm1w02dUyZQ7zOecjemKO6HoKt1PzSD9S1gh9ja6vvWjtkfI68R7/11l/ffekXPmq/x/gLMNetpBv54rySE+y2enJRMlhLlY/1leuRfIeLZ17SrxBsPr4YuqhZ/CxiNl+VK25eHipuHPXqg4hrfdVz9a2fVR4pcwgxqCMfJuianzXWh4/UjQ2rGMIDUB3jdn7yIZd5pr+VDr6NA+pzfWwvuE7djmrD2Zwyz2NkyJz1VddKV5cxtcn60n/Vh8xB2yTnjVupPsgZHM9+GNf8JH3AqcqZNzl3ayRlSNtu/eW8KK/68ta3vmX3+Ec9bHfPe913//KQOukHVvfBHNRnrK4lbXiR9LmXtqv6vc54wpxrrYsHWfcxOqCceam/0u38eQ2dT+Rqz5HzyB3EYN4jY0nGFPS6PhyqS13u3eqZuALf3Hfj1DVQ+2Wsbv9bLwc6oD7n9AHEEf0B9lv3to7pD6xVXfMB9NLWue9+3rft3nndOH+y8V53v+Pub93lg3Yfc5cP3p85+Esv5AL6hZqP/r0PYIy6bi5X5oCsRTm/jhzjK8m6hotjfnF0wUX/dRc2AXCdcsI4GyAfDoeofqsNm87fxK6xt2TzSH/pC3JO+4o62vIArzlJ6oB58LCqtn5RkPSTHKNT0QZ9c6i5CvM5vqVf+wfH5rTqTXcvOqwpWeW31VvHV/FqjV0vDvmQ9LWV66nK5k29q/y72m5Kf3IMnvVPn7b/j1lW8PPpT3nqM8+ubkz1l2sOiIsOLxWrfHMtpf1qn0jadaTdSjd1rIV7BNVmpZt6q1xF3UO5MV/HD/WjcujeJPpc1SVd7FWcY/OU6ueQPfr5Eg7VBp3VX3cB9Os9qdeQuR0aN6/0x0trwjxjnh1LH+e5D6t6zisD16u1kjpwHl+c56+7XDzzkr7gSv11lxUufnETSG4GSLnqVvSNzaGcah7GyU0Jq5h8N76KkbaZ08r/MXLCeO1RzUWdY8aNI4d8Q9pUfWQe2J2NdeW5ou/sAXS6gl7munV/IGMk1c8WmZvUXlQ/+q/9kq257MepyV2tcowOoLfS6Xw4BvnyUF8c8mzO2duUK+h3dLkylj2p1JirXnRrt8a73PXdsdI15jE5J8c8G6H6PiRXyPfY5zAc6hlkfnJsnun7PD1FTnvydF577Lq/7sJ4jXEIc1vlbE6H/KJ/3VP+Oq1r9tcrff06f8x9uAiMC8S+KXH15de1j77zB+2vL4d5Se+ZH3e5QrCZu0XPd9BsChY3hzLwEGDTsOCrDviAgvqwAv14FnVWOYF5Eds8IGPCKj9lY+S4YKvfLf+ps5KP7ZH1Wh/keNryqQbjx/QifSSZZ9VnPP2bOzEY48w1OJ+kb+Wte4EM5spY5p36kjGg9o0Xui5eYl72joMvAtLlAIwLcuaymnP+FGXIWiudTl0b2ZvOT+eDMfvPmAdw/3iByDMcugd55JqTLlfH1E/7Q/tKW2Nwds7rLt7KXswhyZ4n5uqcPqHLOak+Oadenc+8qm+psjb1yFjmbBxQD2pesLI5dN+kyulbP/o3FqQdz2L0fCabJxgf0JEaJ+n2Feck6+p8ZX6dH8/o8z/8amd9FebVwbbGTf8pS7dujxkzLgdjGZfrLfs6rx+/LgwXz7ykXyHyhSsXNpshN3vKvsisdNgM+OXB5OYA/fvwk4wLmRPkvDE9M2YM40jNj7w7PXWMYTw2PVT/dR4Y85xzWzlkjyT1cxzSD6DLFwcePMwRe8s3mB9njtRTFv0D836KkXko196lTC9WdqBsrpxr3qs4XZ+172JU++wd4GfVu/Tf6Ri3ztVc4b09xlm5q7XqdWuj62/6OeQD8MMaYx7QB/z4ApEvElv3wHjWmzmaB3S5Mqa+enmNbhcT3NOgXlLjqVPzyV51cleP86zjzCNjdjlL9Vn16ry9Raf6XslgnrkWAT3G0FvV5ry+kmoDh+7bVp5J1g7K+tQGPalz5uQ3mZA9sMaau9T61F/lnPHRk/QDGdfY6GSMlOt9r2zlXNfQsWPZpy7ulj3UeQ58pM5wcdxwZw8Xhp8EsJAhFzALmjkeZCnnd6NVh4PNgB82DbDZ0j/2q7jY88UG8LPKS5SNgU2SuZGPPo3NuD4yRuYvtY7OX84J/s3D8dqjRH38WY95mmvSzdFD7xM+zBO6OpnnnqzyAeesxTNUn5I14kebTq65ctbOHFa+IfVAv8aAaq+N86s+pB46xq7rrpsDx5g/hTFBPs86Sbp7eV4fkn3NtQCeV/egxssY6IJ5cJ25OqaeZ8m5jCnMdf2rvvUBrotDa1OU8bnSZdy8jMdRc675QfrM2mQ1n75X8rF7AMzZ5z/kvHacQX1AL8m5VW4pr8BH3ieOuucTxmqOgA+p8brcD62NLufMy9rAvKH6yTjKzgnyMWt8lTN66uTX9tUYYJs11p5rm/bA9VbvsLfG4WKZl/QrBAufDehCduELG8U5ZTZBfvrleN1Akj5ybmtcuZsnDnmThxs3feVmrrkB14zXzc3BBsavsZKar+ivmxPms2fGW5H+rIdjS+ZBJtjjXx+Q+dU6t3KpWIs56id9rvqoDTl3sihnjZ3/xD6oj+za5hq7Lre0q/mC8/ZXP5B5o5N+c44x/ADrTh/vybHMpR7OQeqt7iNQn2t6df+2fGCX9ws9qD2FTjfvf8arMOYB1X/uG8B3jhl71QfGutoz34xjfM/Mm1/2qpMzj5xPMh5zdb7LT1+JfjgDOtmX9L2Ss9eM6SvXZwWbVW1buafuKveMmbKknXI+Q6Cun9QlD+dAG3xI18Oax6G10ZF5pS55WbvjnCFtUjamB2RdytYPWzmrh47jaWc+kDElc7Me0ads5YGcdQwXx/zi6IKL+OsuucBZ/N1vjx/LIftu/tiYqQfoutG18xq2fHV0vtjc5+mFPrbsqk7KVb/WQw944KcsqxztGy9UcGydq/FDYHce/aTmuqoxY2SeHeipz9mxJON09wWqTbLym5intcFFjq2ueSHKnoJ9znt7aJ0cQ/UB9pZcur4mxCKu5y26vLbqyjHo6ssx5JpnV0ONY+3WLRknqfWuZNCHNgljmV+dT9KnpO+t+5Nkb6H2JMn+1Bhp19VWOaa3nc4qbpWTVS5bPayQy9Zfd8n6OzJWl3PWxn6nbn0xXmX9reLlfU2deg+l85MxOhm6a1jFTz/HUmPTo/nrLhfPu79tGi4UFiwbQup3rCxqjvrdKzieOjwcVvacO/9bMVNO325SzrlhvXas87Oqo/uU4pheMCbab9Uj6sBK35z0m58aIHP/urwT+2vs9CddfKjjknKlywX9Wlu9D1BzXdW4yp/x1Oewj57T1lzyi5q+IP1KV0t3D5yzTuazNs4XOQbdde0pOAbWcsw6Ya7WnjJ95CUhwa+5ijLj9f76TMq51FHu2KrLsbwfxgR0q+/Mk8NPgKH6rP3jOvNO1AF0rFe9TvYaUk4y38T7wznrRK/rZ/pZ1QDZW8j+ZEzI/qCz6mXNBTpfW3lBp8M58+1kdKpdxld2/pAusC/E9QfaZP0Zo65Vji5n8+Hlmbr1C52sL6ixIO9rztV7uOXHcUg9zvbMvB2rcQAde6Jdh/HVNZeMDdm/4eJ49+oZLhQWLBsicUHnYk49NwCog40P3ZW91Hn8bdnoW1ldwFbYkHWTQvW5qqPrwyovdLX3YWMuW3bCwwYdbJWhi7OCeDyU+QJQ6zYXyZyyT5BzxnesjqcdsnS9TxmOrS3jYn+oxsyVsfTtNfZ+AXM88zIe57wnyuhXG9F/zc+5rNM4zCPTN/wDdsrn0XP91bXEWRmQsRXn3VuizbH7SZCx3bqvmSMHfrNH9VrZe8d83scO8zc3bHJMP6va9G2O2kKdg84Gaq4ZE5TTPqn7FFb7DIztekgdsB+QMWt8/XBgv8pP8p6it4oJ+gV95liNtfJlXlvPBc7dWiFW5nxoTQLjuU+cT13jOw/YATGky0c97aD65QzoZs6gbkWbegbXEnT2K9+ZL3R+zBm9uo45o5fPZMbqvcr4Uv1zVnZe1AVzsG/DxTMv6VcIFiyLXFzwLGY2CfPKiZuBcefqBqv26kGdX8XUBt/KkHly5hqdukmh+kxSJ9G/vdHeM2CDPQ8b/WDDAwGYr7GNg37mjNzpS+aj7Dh6xofMJfU5Q/apy9e42mUuNU7nEzoZH8fWppx6nc9qV30je1Qyr4Ra+IKBz601VY+VnuBPmO/81xfmY/TM13VoHM70hPtLHsjinL5z3rlc16CMbt7H7p5CxhDrcAybtOuuk3oNGUe55pZjsqpN9OX+SGqcjm48Y3IP0VnZ5z23vroO6jysdIjT3auUa81dfurUeF5DxtQ+7Tp51cvOlzJHVyv+AN8dmXPNP+Mk6NX+qattlyuwlyTXU+anTXePXCuSOWsnjOX9sbf2RPQBaQ/66O5J9b/yY345nz5Tt8YQ9bq+6xMyftc/cvCbgLQbLo4bPyWHC8EF68YDxljMjCknLH4ON76btVLteTilvvOHvqNO9AHacnZDmhcb1TxrHuI8R82Nse6Tk5pb+oAaJ2MjEyPzg7SvuWoDjIty9ZG+On1JncyNc41pLtU/NSSMZ22H7sNWbdqKPqrP7h5J3lNjcYb0l+MJ855rXOjWTNWrOsjOcQBn7VjP6Dh+jJ6oa01gT4jP2q1zwny9B6DPPNTVr7Iw1sUQa0BPXc5Se5bn1FeGmnvmls8XoQ7zSLnza6+7OePU+SqD/TPWlq1ok+s8fSBD1g9VhwO/5gxdbDhWJzGG8lY/AZ2tvSv6xV/Ng7M6q354XW1A3ylvPTM447dbD7XXoi3zkr2FLkb2An9cG4szB/Egx8X6wZw54yv1uO56C6tanUtq3V475hk7a1v1OmXgnHaCz9r3lS7o274NF8v84uiCi/gfR7sNt8JFjo2bAhxT5gG82iiwpXMIfRzKE1Y6tQ7HoI4L8zmmj2PryJyU4Zh+AXY8vKruVh7H6mecZKtebRjr+ph1ph/JmF1tK9s63tUoGUNW+Tq+kvmCUGNUW3zW/DKHzkfCF66ut1WuZHyoOSSrOfvIL2zVfmJDjFWfk6y3iw+pI10Pjekvka3AZmsdbEGsjAl5n7pcwdpW88nq/qxQP2VtRR91PNnSOVQXHKvT5WsP00fNY3XP0qc26WdrL9YYaQc1126tV6pepyPEZ772aPU/jkqXS1Jjdv1NH6veMl7vVUfXd6m1pZ+uV6vaOt/Jyi7RR73vHere/c633p8vh/nF0Z75JP0K4cZigXOw8dnELGaOKoM2jLkxcqMjrzZV6qtz7HfUYq5QP3WTlY4+IXOGzK2D+c4HdTjGWWpumRNkPHtR/WjDwVjXN8hxqfr6hqqPf+49D8WUsVnZoQeMJeZb5VU/OGqukLZJjmO39S8v6GVd0OULOV5ldLoYjHPwhQTIxzFBNgd82E/7kGz11jw89Olcog6s+l73BT6In/1crbFq2/mvMRLmVvcF3RwjpnP6TVsObDI/2MoxMVb6TT/GqDGlm1/VJtp4bOkjO55oC1t9Xuk4t6oL6rxy9hS6fO2hfrHN+JzRPc+ntcbP+yPGgVrrVm+rr4yTNnVNpI6HNWpnfMalW1uw6oU+Mkb2oPpgHJuuNscFWft6SNapnPlB9WkOOV9zgfRZZcBuqyeArvqrPa8M+B8unnlJv0KwYNkYwkaqG06U2RDasfA555gbRupmuZyY3caDtD1GB5Rzc2tj/nWczQ+Opw/j1DxqbvowTsZLqp+am6T/HF/pQ6cv+OMFreYOvIRiU+0cc9zYmbd1136kTpdr56vK1QZyHoyrfpev8XMNH7uekflCoo31JtlbqH3owN9WHtlPdSHzg9r37n5U37LSyXFI/8Q1B/qyNec3N+Zvrcxnzc6L8a2xzsOxOdac0m/qZEzH817nfMrmZn7app+tXmzZcYas9Vidug7U27JLGZS7fCs1vrocK5/VFz5yH2WuKdc8D/W2oj2+ujwgdaSOacf9le75YAyOzFu5ux9ec85+gr4S9LJuZdFPzS97mTLk14Wup+rWXJKsJ2X9cmRM5WPue8rmmmPDxXHjVT1cCN2nkCxkNhubrsocwILnwZP2LH7G6uZxTpDPExOqfXKMTue7y9G8eFB144AP/aCzyhXfOYYPxpBr70TfHH5hgZqDHFOLqAvqcq6YM2dtutj2qIstNQ99V51j140oq7tlB/ZUuvuLfSfLyj8yvjubinmYC/quI+yNwRkO+dy6/0nGS1+MGz/zSDLfRNtu7XOdX8Ahc0JmvPaX8bo3srbMLX3nWkyYX+UIXU7adL3UFzBe74v2ytlTa4AubtcLxupalZTBuMfqZLzMFVZ2oK495ch8xXo5i35W8dPn6p56fagn6dPnC9RcuzzBPGBrfakjOaY+eUjWDdU3ttkLyLpAnexB9wxNWT3iM+Yeq+ur5gfmAZlf9rDaopd5Zi6cE3WV0ybHVj1JuepmrtSKPFw885J+heg2DLCgWfjMpSyMuVmEa45u8zDO5mDDVDtZxdRv2uuDeWpwvNMB/VUZ6ssEpE6OJ+jwoOPhuMo1cwPnvU6shTPg/9ieSVeLVF1lY2Z85awNUmcr9lbe6tSjy43x9NXd35Wd85mzsnWBemmTcrLKy7G06eKmrO3Wfak9TD+wdQ+0q/Eq+Mh1DDXXlYwNMaHGxa84fuy6SLzeyi37cEyOqzUl6U8bcBx97IgBmYsyLwT2Vs67R6DmknbqGLOraaVTWdXc1ZY9hdRPuntibhXjo5PXoD0Y51BPIH3UNZB0eWbMLpfU6WTuv3Gwh1vd6t09k+rbdcMYvsy35px2zru+wDlIvTxD9SOrmgAb1jXjgN3KNv2DcvWdcvcs6npyzH03V+XMZbg45iX9ClE3QpILv26ChI2b9uixcdhA2jFHLDYJcH2emCt7cDx1Ov/6AmRz1GfFeXx0/sQ8a648aHg4dDV3MmAnjHc1c06y18TsYkjWbb4Zs8pZV5dj+ss80TmUy3nXTcpSbZTR5ehyVjZGkjlpzxnU52Asc+nsIGPlS02tw7zznDqdT8n6u55DjddhbZAxtmT0ux50ML6VxzG9hy4f9FbzmSNkHilXsKO3tSb9sbedhxo3fWKTedQcVnWL9mkH6kP6O6SzwrWETbUT5KxFuv3ssbX2E/VF2fidb8b0ac7qgXq1H9UX1DqTQzpVzhrpDfzZn/3p/lxJ39plXqu9lTpQbfPZwLHyc+x9z5qg+lzZ1lyg+hZk8/Vaap7MkZNxOYv2CfPYDxfPvKRfIViwLHw3Qt1sKfugqbBJqr1jyJCbTs4Tc8vecXWMufKvT3LMTwOc9zrrgkP+xDzMK+n8gXLadT5qDpC9Rr/7NGVLn8N1UGXQrssRah+d59AGai7Z3zpWfVU5yfjpE5Sxy7r0g03XG6n5qZ/9ga246qFTeyvWkOeq0/kEY5Mb4939r76y7iqv1kInJ+YB1Td7BLutPNIeOl9b+WSMnKuoU+WOWlPd6zmPn624lcz5UN1bPcz4ng/piL45Q70HriWOQ7Vt3X++eUwfSebQyXmPU997UfNZ5aAMnU7Wt6qV6zqfch4JvRFzyHPW2bHV27omE+2M1fmBHAdl8ln1QrZs0yZzce5Qz9VzLGOpL44f6k/mOlwc61U43CRYsCx8N0Eu4Cqj58J3c4sbKT8xAf2yUdJOfTgUE2pc7fUBxmDjsoFX/vUJ+sMOUhfwcR5/Wecq5/SXMscx9tDl6Zz5HKuPf+uoMvG3ckyY08Y5xlb9QyfH9I1ustWTRF81Jgf61gX6BPORzv6YTwKrHXLmytkX8BVdXWAeHF3/nQP9O5Z5cHR1V9n7b74ruWIOK3+H8jDfQ73fyodr9TpW6ynlJGvqfJondlu1pgzpD/usG5iXQ7G1gbo+nD9mHYC65GJM9GsO+jAOmIc+ufZFv/pY5VBl9VfrAB/WRpyaAyg7v9IxVsq1zqwjZeeqLnBPhNiOZ/3H/CsooCvH2mkLnR9gvO49/GzVJ9p5hkO5pO8qH6oHMq/0m3VVn2B+w8UyL+lXCBasG8CF7marsrgJuo3EhkDXDeEcD5LObhVLOVnF9QFIbDclZ+bxVX0nXutb/eQ8/tQVZXOG9Jdyzkm15+hiM54xwDF11XfcvuVcykD8rRwzL6lzaa9/a8j8oPN9TE+qzHrLL+q1rvRZ5yBz9np1z5O0yxjkBPoT8+XMoe86jlzXOVQdzpXUB2ViZU21vqxzJUuNry/PgN0qj/SZPfT62Nyg+oPMb9UPUK59zdhifp0O51UMX1qrv6zb+Vq3GDNf/iTrS51V3atc+MbHGjsdyDjoctSc8QWdj8wh7aoP/LOnu3WAj9V+T31t7N0qFqQMWWeNv9IF58hPuB+OZ/0caZsxu956wCG7KteeSK5B6HSqf3C9rNZYjW8P9K2sP/cIdD7sQ0U/3T3VZ+Y3XBw3fhINFwILloXr5uDMGJstZXETQC72lLUT5ZWd/lcyGJcjH8adXp6h1sF1PmDSNw+PnBPnofqroMcDggeFNugn6S9lQN6y72oBdeqYutYGOS619swrZah5dXrMIeOXWsT+8YWr+0S2+gbGDvVEjFvrti5Bh+PYe06u5KwuxyE7z+aX/rCFzH01jpx9qn5BucsL/ewfB/P6Tbkje5T+laHmgq96f83BM6Q/MUdgvFsnh3JKGTK/2o9Da8vY6RvSd81vFUO9bt2hZw7As65bc2DMmhNkHZmXOXiGzh68rrEdN1eOrWey1HrTnrGsp/rQ/+p5wVHHqx/jwyoW17UX2bOa11ZN4Di2on3VBWTjOU5MqfFBH4fsRB9draA/WNUH6VPQU2ela3zo9gA1dD1arbFaB+ecB+y5Jp7rfrhY5iX9CsGCZeGyiFnobHRkcHNI3QzY+mCodltzOe84rOQal83W2YM6gI61VT0fGvhFR/Cdc/gzvnqdvy5H/HCtvjbVHxxjv6rZfEEdx1I3a6s+oNa+yk/ZXPTleO159VvtkpVvONSTVX9q/KyB86F5jvSpLhyyQ+76BNo653yOr2oCbVJHvZoXZP8g9VMW8+ecPYJO1oeHcRL8+KLV+ai9cy11HJMTKJuXZD9SVm/V+5XvjswRmdrtS851dQM6+F7F1Ffnx/wTc8jYUO3Bmrb0OJD5RgL9LqbUevP5gq3xUhb7cAzmVO9dxt+KVWvMnlXdrZpA/fwk3f7m2VigT67Nb7UW0/aQXeej1pr+oNanziofr/WTXws6m+qf+dwj+uGMbvpJqo+MkeAD/8PFc8OVP1wYLG4WbpVzcyiDmwHU9wEm6K/mIOeBjVxjpQwZt9qnDSinTuJDAzqdnJNVPGVIfcg4YJ2gv2PtV/Uwz0OJBxeoU2OLupk7Z9GmxmL80CcZ0OXIvA/Wzo5z5yPnJetiPHW72JJ1Scqr+ewtGN/xQ36Ru1q0xU+O61+/q09S1edsDEn7zAVy7rz7DrusO2WO9Kc+eJ0wpp0HdL3bYpWPsmewrswnY6eMThdfnRqr66PoU/Jaf4c+iTZOjZljx/gR8tPGA+y/+TuXcUA9ronJGZutmJD2qbdaix0538mwysNaVrGYzxyPYVUT6JeYgr7jmW+SecDqOQDYoksPXeuAjjmlLBkj43e5QNXRl7l0eaVOXifp33nHOOea7vy4Njmv8pLMb7hY5iX9CsHidhG7MYQFL8ro5JEbIDk0xyFsqi4W1LhVlrTxi0bVcYPyMIMtHTY8c27+qncoR/1wVuYhm7qMw5b9Vq5i/3xYaQOZB6x6nblacwXbQ/3ocmSMeexXdpA+zLfLz76gp7+URV3tMveuDn3knP3CPsnxzq7zX2vFNu+HdSX2rNoC+jUGPmt/nHfOWjI2dHLaQ9adcs5B7buy1Jwy3653oK6+kHNPZXxkPyBwDLr8jJ+YS5Lxs/bLiZG+AB+rusWajIls/cf4qTHBsdr/nONsjcjq6Z85yDFJH8pdbvqX2kNR7nRBufpPDsXi6Hpo/up0+hXtuU9iryHzdUzfuV7ImfmtWrMu7DP/9A8Zw7msWV31HF+trcyr+/pbr0HfnAHfWbNYO3R+mHev17nsh3Ey1+HiuPGdGy4EFiwLm82RC9nNwIZk83gNVVeZAxkbzujneJWTGqvGzZjVhzrasFlTRxmol3k4pMNY6kvNT7nzI/ZZfXRqjWCdkHnUPDkn2KPrw2qVB5iDsaHmWmsGfOo/MX/r6vI0TpJ22Uvsam/y05RDfVFWV9KuqwOYq/WbQyXH027lw5qyNueg2iTVlnPq15q3PnVLMq8qc9S9Ds5VGbyu90tWOWXd2B6TP3IXP8FWndStfrxvNWbK6gJj6Y9z9g62YjgmjKvjtfEr+gdzcAx9X95X+aNLrjlW+y/miA/jrJ7FnQxZZ42VmFftobniE7q1WuUup2QVSzLPrVok9RPjEkvUI64HdM/+Ss1bW8CecebTvnB6nDEAABofSURBVLtfkDqM1+uqV3XEPMyr+uDcyYA/6eKvbDkfIvuTcchxuHhu8dfXcSYPwS1ucYvdTWnNr7zh9/cLmMXswmcROwaOew25SdicbuJK+q0Yp8qQdjWPZJXrilUNSeocAh+Za8I4DxS+6NUHG6RNl9fKr9T+ZZyV7yTjwCpX9DJWzTXvQZdvl1vaOFb9ylZ+XbwE2617IF1OknNQ5UO+OzLvzsdWPh3pT32+OOOzm6uow3zK4PVW3ejUfGvfMw/wubGi6gO+O7/mneeEsZrzofw6Mv4f/fGf3mhN1Jq2YtQck9SrfV/dg2RVS8ZUJ8fIF//pu9aLfvrfev5D9qzmio01mUeXV+c781jJSdfHQ/cL0he+U2errpr/A+93t91Lf/SVuzvf+SP3Y+aZ9RsrbTuO1RP1ky3b1D82hmCbtWyB3qGer+jup3J3T0C/d7/zrffny+GmvnPdXJlP0q8QLmxwM+YYMF43Ktc84NgQbgb18shx9R3POMjqOZ8yIG/5AG08Uh+ZB4IbtdPhgNWnRRX1Oz/ok1/3sAD1OBKuzbXmv6q9xtEvR9aSOC882A59gql+NwfMd3mS28oGMg/g2gOwXX2Kv+qRtqu6UobMaWuuyuZ07JoR80sfq5iy8me9+gR95twxayFlUO7qXuXLeL1f+vUe1Zq7nOr9RKf2i3nq4qwPc7JeqHZ5DTW/rfisp6wXmfn0txWDY2u9qAM1jqTvlX23H8T5zIF7xlj6Vuasj/StnjG2elbrBeYS7RJ9pm9I3SpX3YxjLXlvzDPHQL8cqbNVlzG5BnJJnIfMi3F0qz/9SNU7hPp5X5L6XFBnlUvKFX2nD+PWHLDf6vnKFrJvVfb+1Hz1MVw885J+hWDBsnDFzeFG6BY6GxrYCDzUGYc6D2mPPhsI2RjGr/HSR9L5qLaclf1iyrW2oB6kT0ldqHb6T5lYvBBK5gadzVad/rN1zR9Z37V/kHGgq1udjI8efrq6jQf67eagy3PLpsuljqX/SsZLWbbqgpoTcSXnstdd340tyl3PjVN9QM0HtFX2rD9xTJ1K5qhe2iinTzCXru4u35yvkEM+N6DmJPV+Zgxhvus9NjmedtWPdadNlUE7j64foo4Yw952OUPei9WaU06qPdT8zaHOg7kylnkr5xigV+8j1JjYeRgLMq6+M7+UjZW+na9rVVLXGOe5X1BjpI4yR60LO1CX57jkfUsfYt6iXPvi14ZurspQ70vOZ0zGDq1ROCY2fjJuzaHWDulnZavdan+IOTKGXOsZLo5+Fw43GR98wIaqmwxyUbvQEzZG6jK/skeXzWSMlX6OcU7YcMbUTxdLGX03rufUg9QRrs23s6syOpfTS+c5V8zL+Cmjrw+vuzigTRe/Ys2eoeZoTziyVqlz2UcOcA5qL3IMMn7Kkn5TThjLPLqc8GmPHOdw3BxXvUM3/YL+IH3k3pO0R4cj++H8ob6BY5yTVV5SfWrP2TnBl4d0a18fiTZpn3lI1w/l7LN6tf+c7VnnAxmMzVjmpFzXOefaD+l6AF3/Ml+O/EY/9VcyaAvMJcaodUraijlnrXlOsreSMXM8a1VmnqPLr+Yq5msftM9YkLUxp76kXSdDtZG8xxmHmoQ5oFap8Y2lLuArewW1LxmzzknKoN+sDawBGKtrq7tvx8TWD7rqp7y1T8C8OlvmjJGyqJu2xMv7M1wc8zPpZ7zuda/bveQlLzm72u2e85zn7J761KeeXe12n/d5n7e7733ve3Z1mPyZdGCxC5vRRc/mWf2cF2iHn/QB+hbn2Sz6TJvOB7puXGXzq7ZdruhkvMS56r/2xOv0v9WXzGurl6nX5aG8iiPpJ3tufcfkXOlqYCzrAfVW+ec9rblBzkunV9nqETbOH4qpnD7O06dK+oXz+tIeaq+hqyHvj3X4Cd6qT5nXoXVZ8zdOvd+ZU9LpKlfflc4fdL0B9e0/rHwIuvag+3nzrOtyc858kprvedYLtufJp/ak3gtl0Xf+THpF39qr040zVucT5rr6zdVccj79ZA1V7nweIus1h6wF0rdj1c6fSb/rXa9d5pC+ofraWhc5d2j94Je9Yx9rPzsyl628VrGxqfdDuYJf/XT3OvvdsYpl7uf5mfSLfue6uTIv6cHtb3/73dve9razqxvyxje+8bqHwF3Prg7za2/9k/3ZzQZ8t8nG4JM+qBtyhXZuLO2T1OEFovrsfBg/WeVSc9VfPgzO86CopP9j+nKeXnZ1VlYPHqn1pn6XM9edH2Cuy3NFl3/a66/67e551tHpbq0Lxut9TR+V2jN1M8/qs5NXMczzkK9qn7Vuob/VGvM6YS71qk3S+cv8gTnyzT196F4lne+aS/rLe5a1Az6w9Zx0PmrfVmSOcChn/buu7deqPunylqwb8j4cm09n24Ft9oTr9FFzrLoJdt3zHvRZ74O6NW/o/EDm0HEofidv9Yux7msZtm9605t3D37APc9Gbsy3P/cFu89+5GP2Poi31T/IviDnPa5zKafeMZzXposN+qhypYtRfXpOP9rV8RoLPe5HfmDx8Xf7kL18LBf5znVzZX7cJfi6r/u6M+mG8N3deRcLC7bCd6f50GCRuyGEOb7T5azMJsCOM5tE+9TVN+fqE5xPH8YnV777X+XCRlRX8JebmoOHqjo5l/6dT9+QcylL1gqHeln1zaHmok0+fJRrvNSxVu1TlurHnKDmV3E+e1/vkzqM6Tfp7nnWkfEd53oVD7RVB8yDszJ5G7/6SBn0CZ3c+YbMQY6x39pHyvY99Wo8r2ufUi9lqP5zDsw55+hj6h26V919g0P9AH1j7/5SjzHAf45zzpxSBnP0yPw4pF5DzRnwT27GkarLkXL1nax8HZtP2uazobsv2Nb600fNv+o6zhm7bhz06XX6gIxZ56D6M/+upg78u4aqvOqXOTCPXs2JMf6Ky+O/8AlnIzfk2muv3X3O5z52n5O1V99ZF0etwdyy96APbCD19JXUa+hsqtw935Q59AHKjOd94YDOp6ScfpJVLPW8RxypeywX+c51c2U+SS9039lxfdvb3vbs6jj4JJ2FyyZxQSeMAxvLxZ1yJX2w4bY+AcG3vrrYiXms7OGQjy2q/5q74zXmVl9qPtVn1ZdDdejHLyZSc2ceVjlnnPSzxare7A9w3d1/YA69jL+iqy/JeMlN7TV+uz5lb1f3QbTLXFa+tuwTbHhZlVX+NeaqT5C60N3XjlVdKzKHrXzg2H4knf/Kysehfq16lP4yZh2vcVf5Sd6DY9fhsfmkLWStWzVkHl3+6qdupY5nDFjVIqv7UKm5d76OpfarY9Ufxu519zvu5eR5z3/R7qF/9+9dyuu8dam/+hTfOfM2H16Os5bM09zFuRWpC1lDzbNba1DrZhwd8jH/mlcXBzJW9Zv9RD7vJ+lwUe9cN1fmk/TCs571rDPpeviO7nIWCwvWjdN91ywucFBmg2BfvysWP4lgXj3Rt75W36VL5x8ylyRrWPnM8eo/P0Wpvh2HTq6+JH1C1fcgr0rWox/ktJOcFz8FAuNmf/I+rmSOVf6iHtQe5hx+jb11n6pd1cm5pPY6PwXLmraofYLsbXcfOt+ZS+Z+jL31ZvwuhnrVNzC+VW/qgnLV73LJGIynjnJ3r1KW1Hd+1Q99JukzbS+iX6seoWutXRzw+lB9KW/FAvPhenUfVvmgny9u5pJytYGM0eWcqFv91fHKqhbl1X3IOBzWBl2c9NnJub5qvzodyLyFsfpp+sfe8967R3z2I/eyPrfq6npsTpxrffryTAx0OHIMtDVe9mG1NpUr+gb708UzJqRNjjPW+YM6ru+MlTrQff07Lxf1znVzZT5Jb8jv7C73Ozp/Jn0LNmV+d4oMufGOxc3ffZef6NOYbixskTPmSqeijTmoc578IfvQyVu5QtrIVg21HvxRg37T9thaVj1PvynL5dQLVXeLY+27Hm3lC9bdxejIPh2yOeT7PPPIh+471L5U3/qEQ/3KXlW/XS6SMTrUrTWt5NQHrqvtMT4h84RVv/TDc6l+Mplkj8wvOSav1AGuU5ZVrFVugM0x/9LSsbrn6eNQzkn663S25rNeSZ3sTV6v8l3dixWH8oVOp8v7Db/2/+we/uBPPLt698+iQ/VR6zrU40Ngj61nONSrpNqmvEI/VW8V9xArf5nvMf54ofe943I+SYeLeOe6uXLjj02GSz8ndVO+o+OBxXfFnlnsKXOwqdgQ+Z0qOJ8wl9+N53fAoL/0pZ+MK/U7YuXuO2hRXvmE1EkO5Q/E8wtnlbdy1R9fRHlYJNW2+86faw58UJN+07bGWsndvQbPkLJkrK2cMyak7mqtKXekvTG6HtU66XW+5KCvjWSuVe7Wjzp1XRzyDfhThm4ev/jJevVb/Xd9SbTlUA9qv0BfXNd7mzGMY+5b91Jd6XxC+hdkDvPzfh/js+rIql/IjDO/soXsEXocx9Ta5Z7XdQ66WOrYe84pm785JSsbZfZK5qyceuk385H0m71mrHuOdjGQD62j7E1eQ5evc6Bc/a9iScZIHXN231Zfd7v7x+w+/UEP3evyKTo/iw5dnFqX/hLjWeOWTA6ck9or74uxah8yfs0FalztK6t7VOVjnqvguHOHfBE7c7gcLuKd6+bKfJK+4K53+ZDdK3/m5y/7lxf8mfSEBc4YZzYci1odFn1+muB8lZPqP8lYsNI1br5wQeqnDhzr86bk37HKVbb81Ro60OFhU+vrYgHz2NRP2Fb9WfWly7vmi8/sozbq8bJCHo6jv5K34nZYTyV9QuZX7zm6Xa+g9oXxzBO2fFfSbxcPakx9HqOTcq1hax8lqS81Hrb6qnIl/XXyqoZufaX/zhdrTZ81l4zX+al5dLXAsbVCl/sx8VY6gi467quaU8Y9RMYVfcvKbxejy6fifHKM3YpVvpX0X2Nxfd57kbaQ136a7s+ii7EzRnLo3h9LF6fmKfZvdW9XcrKqB4y7wly7OPo9ti9dbdhd7ifpwKfpr33ta+cXRgvzkr7gDW/9w93d7nz7s6vz8Ywv2d4swzAMwzDcdF71ut3uQfPntE+CZ7zg8l8n3/72t8+n6A03/PeP4RKX+4I+DMMwDMN7hnlBv3kwL+g985I+DMMwDMMwDCfGvKQPwzAMwzAMw4kxL+nDMAzDMAzDcGLMS/owDMMwDMMwnBjzkj4MwzAMwzAMJ8a8pA/DMAzDMAzDiTEv6cMwDMMwDMNwYsxL+jAMwzAMwzCcGPOSPgzDMAzDMAwnxrykD8MwDMMwDMOJMS/pwzAMwzAMw3BizEv6MAzDMAzDMJwY85I+DMMwDMMwDCfGvKQPwzAMwzAMw4kxL+nDMAzDMAzDcGLMS/owDMMwDMMwnBjzkj4MwzAMwzAMJ8a8pA/DMAzDMAzDiTEv6cMwDMMwDMNwYsxL+jAMwzAMwzCcGPOSPgzDMAzDMAwnxrykD8MwDMMwDMOJMS/pwzAMwzAMw3BizEv6MAzDMAzDMJwY85I+DMMwDMMwDCfGvKQPwzAMwzAMw4kxL+nDMAzDMAzDcGLMS/owDMMwDMMwnBjzkj4MwzAMwzAMJ8a8pA/DMAzDMAzDiTEv6cMwDMMwDMNwYsxL+jAMwzAMwzCcGPOSPgzDMAzDMAwnxrykD8MwDMMwDMOJcYu/vo4zeRiGYRiGYRiGE2A+SR+GYRiGYRiGE2Ne0odhGIZhGIbhxJiX9GEYhmEYhmE4MeYlfRiGYRiGYRhOjHlJH4ZhGIZhGIYTY17Sh2EYhmEYhuHEmJf0YRiGYRiGYTgx5iV9GIZhGIZhGE6MeUkfhmEYhmEYhhNjXtLfh3j729++e9WrXrV73etedzYyDMMwDMMw3ByZl/QT58/e+Ve7Jz3pSbu73vWuu9vd7na7Bz/4wbtP+IRP2N3ylrfafeInfuK8sA/DMAzDMNwMucVfX8eZPJwYfHL+uY/9/N0rf/LHz0ZuzDXX3HL3mte8enff+973bGQYhmEYhmF4X2c+ST9h8gX9qU996u6Nb3zjju+pOJ73/Bftx9/5zj/ff7L+pje9aX89DMMwDMMwvO8zL+knCj977gv6ox/zuN2zn/3s/Y+8yJOe8Ljdd3zHd5xd7XYveclLzqRhGIZhGIbT5DGPffz+x3Wf85znnI0MK+bHXU4Ufg79O7/zO/fy2972tt1tb3vbvVy5/e1vv5+/3/3ut3vta197NjoMwzAMw3B63OIWt9if573lMFfFJ+l8t8Z3bZ/xsEcsfyyEX8BEh+O9/aMj/Cy6L+gs4tULOtz//vffn3/hF35hfuRlGIZhGIb3CW57hw89k4YVV8VL+qd8yqfsX2L58ZFHP/rRZ6M35Au+6EsuvejyV1Tem/DJuDzsYQ87k3ryF0bf8pa3nEnDMAzDMAyny9v/4HfOpGHFVfGS/qAHPWj/c93Ai/iLX/zivSx80v76X77+Txm+7GUv2/zkWvi0m3+yOc/x2X//MWfW2+TL9n3uc58zqecjP/Ijz6Td7rd/+7fPpGEYhmEYhtNlPkk/zFXzi6Pf893fsbvlNR+4l7/8y798/5INnJ/2tKftZV7keaE/hmtu9cFn0vG8/pf+7zNpm1/91V89k67Pb4v8huKQ7jAMwzAMNw/4MV3+yATHCt4L1Dm1d4T5JP0wV81LOi+z/+QZ/3Qv8+MkvpjzZw6BH3HhRf5YbnXN++9+8Rd/cffTP/3TRx2vfvWr98cx5Ea6xz3ucSb13OlOdzqT5iV9GIZhGK4Wvuu7vmv/HxxyrP5SCu846rzht/5k9653vets5r3PfJJ+mKvur7vwi6H8yAvwZw19WefPGT7xiU/cy+9t2GzmxQv+1qf7fHfM5gPq4e+pD8MwDMNw84b/kfzDP+yOl36Pjf9LJf9Uc74fPOUpT9l967d+614+hO8fx8KP5T7ucdf/SPEx8OO/MH/d5TBX3Us6/zzEf/6TnNpC4S+78CcY4Twv6af0jcYwDMMwDFcWfsfu8Y9//F7+rEc+evdjP/IDe5l/Wf/4e91n95tv/fXdtddee/Rff0Pvoz7qo86ujuO871C+pD/koZ+5e8W/+7d7eei5an7cRfhrKPVF9tjvLt9T5I+45M+nd+Qvix760ZhhGIZhGG4+8Am2fxjj3/zoD+4/uINv/uZv3r+gwwte8IL9+Rj4JB5/vEDz8s35/g/4tN3fe8i9l2OPecxxfxSjMj+Tfpir7pN0vrvku8T8M4cssvN+N9f5OQTfHOT/ErriPD/Ckj8aw8/I559kHIZhGIbh5g3vI/7paD41/+Ef/uFLPzFw7HvHe5L5JP14rrpP0nmh9cWaBQL8/fT6ZxmP4Twv6PATP/ETZ9I2+aL9k6/8mTOp57W/8B/PpOs35zAMwzAMVw/8YQw+0IM3v/nNu4c85CF7mRd3x0+R+ST9MFfVJ+n5CTWfTn/913/97sPu9Dd3f/7Ov9wv5j/8wz/czx2L/6x0LPxN8/ylji3yF1y3btHtb3/7/TcL8x3pMAzDMFy95HsD8GMuX/zFX3x2dTrMJ+nHc1W9pPOCzHeZ+UKev6R5Sv8slD/GsvqF0Mz9RS960bl+u3oYhmEYhpsPn/GwR+x/MkAu949J8P7xjne84+xq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alt=\"unconfined aquifer with soils in parallel\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L)\r\n% h = water table elevation above the aquifer bottom\r\n% Qp = flow per unit width\r\n% x = locations where WTE is requested\r\n% K1 = hydraulic conductivity of upper layer\r\n% K2 = hydraulic conductivity of lower layer\r\n% b2 = thickness of lower layer\r\n% h0 = water table elevation on the left side (x = 0)\r\n% hL = water table elevation on the right side (x = L)\r\n% L = length of the aquifer\r\n\r\n Qp = mean([K1 K2])*(h0-hL)*b2/L;\r\n h = h0 + (hL-h0)*x/L;","test_suite":"%%\r\nx = [0 251.884 503.2297 754.0371 1004.3062 1254.0371 1503.2297 1751.884 2000];\r\nK1 = 900; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 8000; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37; % Water table elevation on the left side (m)\r\nhL = 33; % Water table elevation on the right side (m)\r\nL = 2000; % Length of aquifer (m)\r\nb2 = 25; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 418;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 284.1463 558.5366 823.1707 1078.0488 1323.1707 1558.5366 1784.1463 2000];\r\nK1 = 8000; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 900; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37; % Water table elevation on the left side (m)\r\nhL = 33; % Water table elevation on the right side (m)\r\nL = 2000; % Length of aquifer (m)\r\nb2 = 25; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 205;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 230.8945 460.1048 687.631 913.4731 1137.631 1360.1048 1580.8945 1800];\r\nK1 = 4; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50; % Water table elevation on the left side (m)\r\nhL = 48; % Water table elevation on the right side (m)\r\nL = 1800; % Length of aquifer (m)\r\nb2 = 16; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 0.1484;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 225.2925 450.5015 675.6269 900.6686 1125.6269 1350.5015 1575.2925 1800];\r\nK1 = 0.1; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 4; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50; % Water table elevation on the left side (m)\r\nhL = 48; % Water table elevation on the right side (m)\r\nL = 1800; % Length of aquifer (m)\r\nb2 = 16; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 7.48e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7; % Water table elevation on the left side (m)\r\nhL = 2.8; % Water table elevation on the right side (m)\r\nL = 20; % Length of aquifer (m)\r\nb2 = 1.5; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7; % Water table elevation on the left side (m)\r\nhL = 2.8; % Water table elevation on the right side (m)\r\nL = 20; % Length of aquifer (m)\r\nb2 = 1.5; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 2.3183 4.6126 6.8829 9.1291 11.3514 13.5495 15.7237 17.8739 20];\r\nK1 = 0.1; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.5; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7; % Water table elevation on the left side (m)\r\nhL = 2.8; % Water table elevation on the right side (m)\r\nL = 20; % Length of aquifer (m)\r\nb2 = 1.5; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.163e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = 0:325:1300;\r\nK1 = 5; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 5; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 10; % Water table elevation on the left side (m)\r\nhL = 9; % Water table elevation on the right side (m)\r\nL = 1300; % Length of aquifer (m)\r\nb2 = 4; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = [10 9.7596 9.5131 9.2601 9];\r\nQp_correct = 3.65e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('unconfParallel.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-30T19:04:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-30T15:05:42.000Z","updated_at":"2023-09-30T19:04:22.000Z","published_at":"2023-09-30T15:09:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e varies with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, so does \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff} = \\\\frac{1}{h}[K_2 b_2 + K_1(h-b_2)]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using Darcy’s law as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can write the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e through the aquifer as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K_{eff} \\\\frac{dh}{dx} A = -K_{eff} \\\\frac{dh}{dx} h w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(0) = h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(0) = h_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(L) = hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(L) = h_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to determine the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the constant of integration. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"341\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"559\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" 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Sequences 110: Integration of the Sum of a Recursive Trigonometric Function","description":"A trigonometric function, , is defined as follows:\r\n , in radians\r\nApplying recursively we define another function , for integer :\r\n \r\nWe then define as the sum of value of from to :\r\n \r\nFinally, we are asked to evaluate the integral of with respect to , over the real range :\r\n \r\nFor example for , , , we have:\r\n \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\r\n a = 7.05797686912156\r\nPlease present the final output rounded-off to 6 decimal places. Therefore the final answer is .\r\n-------------------------\r\nNOTE: There are a number of ways to do numerical Integration in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the integral function shown above.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 507px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 462.578125px 253.5px; transform-origin: 462.578125px 253.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA trigonometric function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"19\" style=\"width: 137.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in radians\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eApplying \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAmCAYAAABzhkOMAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAP6ADAAQAAAABAAAAJgAAAADyFT37AAAEHElEQVRoBe2YWYhOYRjHxzb2fRuyZi03lJLCBRqFcWEpDZEQJReWuxG5kISSubDFlRsllKUkM1nChaUpW7LUZCt7ZN9+f877dead95zvnOM7QzlP/b/vfZ/n+T/v9rzL9xUVZZLNQDYD2QxkM5DqDJQT/T5oW6BWrhJnddxYTS1CCfXeli5u9S2E2yGkZdgqwWIg30LISoKcBD3AqqQBKyD++ENcCml8FLbPYEOIT1LTXIjfweyoAeyVb+0jnqVcDV6BD2AWmAgkGsBy0Ax0BMPAdFAM/DGo5kR+B8BxsCanLVxhP6GGgD2gBtwCsWQb3lp5V+ps9Wyy3wG2jEShSblnG7z6Eb6/gAEB9kKoWxDkMbgJ2sQNqFnTQdTIQcw3eFF2gacObjk6TZripy3KSLW1Pl9DjS2HVtRPAZGTyAlILR3EhZ4ujb1uN7cbxXMwH7gW0fbP1YdS6pmr1S1EWXmlndLfL7o9voHrfmXKZZ0tWsDxYe3YK68rSnsmqXyEeNkiz6Gudk5b+rCqsqcMrAUVwN6/k9BtBtOAS6o85QKXMYkuysq74p5BqVUI6qjN2YRC97+yRTxhCzDi78c7lNqqtgxGId4j25C07m/0TowgD/BVRwZG5KjjWuleQIMT11xbKzzdPr51MOt8con2+legCbSvc5d/Xl2SwasTn4AGoHs+rhyGIK5QCrStlPJR5BlO4vUJcrb3fJBfUn1XiMVAK/A6QZCzPo6er5VA31HkheekDHJK2oPv4bWqgWsV4soFH6GW8jpfPV/RTHZgxqU9eO1Zia7AJHINklJdcgW8/1WK9mHeG9r7Tkl78Oa01Xu/ubMH4UodVmYCR4e71rN29jQP61k8RdqD16rp4JGYzvyuRfvUFdfFcy3hO+qNIYrh/bXBqxOm8aCXo3xcMhXlErDDZxzrK4cVtc+VacqaN0GOcVbev2/1UzaqmDs6ascVtzvYC7TyeuGZw9LEUPs7QSfgknGessZlTKI7BEmdEPQCawKiyGScxDka4twU2xQwCGiSz4OLQHqJBqEYT4B0GngV0DvCJdtRyn+pyxhHp/QpA9q/CmiwgXIHkE80SY+B0s8MxuboV5+Jq4nVOdHX57TRZ1cs3eF+u8/1V/EGn59AUGbY/s66/p35DkzHXN8Hncy6Sr3XxZ1XV52r6V8iE/slZftk749Og5GP/lky6U+xnoxBIz9l6j8h/eiFVv4uCFr9UdhKgeuHCuqibkAZqFdjmFRjVJaOCHNqaNsMGtSKLEqx4QleG8tSbCNx6K0wtaeHJ44QTNRVWguibMPgKClalPLnwCMQ+IMjQftt4FwF90D7BPwGo+jlpR8sur50ExRCjhFE/zEMLESwtGMU08BMEOeRFdYnnSftwhwyWzYD2QxkM/Bfz8BPP8zkcVJh+/8AAAAASUVORK5CYII=\" width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e recursively we define another function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, for integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 51px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25.5px; text-align: left; transform-origin: 384px 25.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"166.5\" height=\"51\" style=\"width: 166.5px; height: 51px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe then define \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"19\" style=\"width: 44px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the sum of value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"46\" style=\"width: 129.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFinally, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ewe are asked to evaluate the integral of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, over the real range \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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width=\"204\" height=\"48\" style=\"width: 204px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAASaADAAQAAAABAAAAJAAAAABLVRfgAAADIElEQVRoBe2YW4hNURjHz8glMjR4MOX2Jinx4IEXuWvyIkXxMkpKCXlQLqVEpCaePEx5kFIoeSO3TiglyjXhiaFIcr9ff/9xvvrObu05e5+hmXNmffWbvfb3fWvP+v5n7bXWOYVCtKhAVCAqEBWICtSbAg31VlCFekYSb4HJMAyuw1W4D9FQYBW8gt8BDuDraxOGksttBbcS5wMcgzPwBrxgO7jvs9ZM5Z/gLIxyKgykvRFMqNsu1ueaO6n4GgxKqfwefhOqMZTTL+SsM5/EaYWvKXW9KPm1Xul1jJZQQAJ+BM2ko4lYplu9v/NhMyxxPcbTXgf7Ya7z12JzKYOWQM9hdJ4C2kh+Cvae6rqy9ABto5qSPja9FKu1i85LWtD1mo3NO/iJdFgG30BifIcmWA8/QDPoNJhQa2lntZMkalDdpTszWDNmD1h9quMSjINcNoDs96AHXAS9blJ9Acg2gIm0qNOT7c8518/6V3PN8z/9yLRM6EMP/c8O/EN9srX7WyNxncG9ddD54TCsAZ01ZFP+Xjr/3nLtSs29JJyolJQhfiNDTijlEE69Bfp6Mhu2g9U5hvYW2AaZbBdZpvZj2u2JXg9K8bsJf63dTmDA58FqfZinAB2+fMchrrPeXYu1OX+tNhsZuK1PWnN1Eq9omoo/wYSYk+ix2sUWJmK1elt0Nan+MgutSfPIsJO41iAt3N50dpJ9Ae0KeUy726w8HVJytfteSIlV475MJ43rNWjnLbOQSLaDKVE/IXiTeLb96sGffTBDW1N7RIa8Sinaff+l2ey5E3poVyK9pIO2bG/TuLEHapbJtGMcgSJUsp7e3ULjk+A2MZKTIpRfmITX1qL2QIb/aUGC7YZHMDyQ21tcyxnIKdD2PjgwqK34VHMxEAu6vAiLAxn78JmIet3egj8zBbr0uKuDEdiYn9BuhWbQh3wQFNO6q6Ugkx0nS530zTikegv+X6WcZ1xnQm+3TQzQRPLXd/ivgDaBBki1LoMpvexH9JvE8y7cKY/87259H50KTaCZpUOwZpVEixYViApEBaICUYGoQFQgKlClAn8AYTTWbkfCa8gAAAAASUVORK5CYII=\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"20\" style=\"width: 50px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 459.578125px 20px; transform-origin: 459.578125px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e a = 7.05797686912156\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAAAkCAYAAAD2DsoUAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAq6ADAAQAAAABAAAAJAAAAABWABvBAAAIsElEQVR4Ae2YacyVxRXHX8UVUakLFQiYKO7GGC0VrLh/QDRuqHHFV0lbW9u0EjXEpTE2ccfli6ZWiUto3XBJ3Ve0FfdiNVglLS9KXaOiiKJWaX//+85cD+PcZ+be54NemJP875w5y5wzZ+aZeZ7b01OoVKBUoFSgVKBUoFSgVKBUoFSgVKBUoFSgVKBUYOWqwCoryXS3Y54DM+f6AXbzM22t2VA6h4FR4GvwMJgFPgMpGobB8IiR1mcXMAHsZ/SD4bcw/RT7EgZfBEYaeycwBuwA+sBs8BxYCmJUJ24d31guK6RsCLPSQv0vE9M7qMKvXYxltLOAFl3xPgeTQIqewqAqv5ODAS5P2IdjjQz8N6Z/vxvjRdqZ4F3X/w/taBCjOnHr+MZyWSFlU5lVuHhV/WParMJk7LVJhX2M7/7wiqNT9lgjD9lxCKryWYx+XeO0NvyihI8db57xFatTXBtSNtOAv13V/tnJdbJOBJbqxK3j28xhtSa3YjKrMq2fARX/jyB2HSLu2Q38HHwJ7ga5tC+GVwMttNpHgKd7YKaDE8F1YC6YA0I6HcFX4CKgjR3SvQg+McIj4QeD58EM8AHQxgvpKgSDwO2B4kL6euXQmOcA76u2F+wItgbyfwAsAaI6cev49kdfCX73Y47aCNpUVXQFSi2WNlg7pI0tPyH2Drml0V8LH9K2CHQi3xgqKvrPoHsQrFFhszE6zVt5jTZ2ekdVPMlbxfyd08vmLOCpTtw6vj7+Ct9OZoZnJmapU/FNoMXRKZhL+qDyG+KtCqd30GlsfWhtENjp5JVOH2b+Og5MluuuRU+nt2JXkW4Tjft6YDTFyaXTpoyRPrakF3Rqi+rErePbH738NivwEzgtzH/Bhk1pmjkVE7+oN1WY32Ls7IfSMOT2w08b4y/gOLAOqEMP4azcLgsG0enuc9aDHKPVEXobtcozl1rFzfFP+uqdLod05ejpPxdcAsaCzYEW7FKwPuhWOtwl/jitP0ly5qITyNM/PRNp5xrZ1ob/Dby9ynXqHgBuAAvB0aAT0ivAXs5xZjDAKNNvtWZ6aBcbu9jrjVE32aq4TaMWTJZvzmadSABdJzoh9gSbgQfAXeBi0AuWgG6kVUhaD6EoXNh+aevf4Ub1keFD9mMjGGn49+CfBbHa/QD5DHA2aJcOxmEAeAfMDpztwzgi0Nnu+6aTu1mr4prhomwd3+aAp8EtA0reniRn0PdXxW3wuXQ7hipYXeyTGzBhtyt6zeNrsEnCNlTrNPU1OD5Umn6vsZtj5J7VA6NNPAn0AT+mbw9F1g49iLF8r4w4TXM66ecBxY7Riwh9fN0AOVQVN+Vfx7cxtv66UML6i2N0Q/LNjwrrJ6O/fHLJv5d4307b8bkBE3aXoVcOf03YxdSLnK/8dTK0It1Mfp5vtjJy8jVp9VeWfZd9lX7ODaghNgK6xhUv9kCPczqfzwT6IQ1EoDX3NoeEBpF+Km7EpSnK9l2t6bI8cwzdk5zol7TPLa/u2db0HzZ8ir0Ag1tTRhn6FzJsUiZ1XgE09lIw2AVpdUJJbWus67mKtEkvAtos/mTcCn5X8DeQIj00iqeb6/GIsR5KQZtW9CdwIHgCaA7bA8UfBDw96ZmKNhW3wrXxoFflXOXbWAC97+jJ0lUXe6rvc/o+2m4lfST600PXcLukK93791Y4S+ft/lFhF6puNn46PHJI3xKKNb3CWCfZy87O5/UWfX9TaKN7+WvwOZQTt9U42b6xjajT74du5HNplwVR1qM/1skeC3Td1D3cJfs87RsdJP6u8fEnrBE1Wat7uylNM/ZbYEjavPG3297ObmaF/fvo9Fqn17dZYD7Q4aQD6BfgauAp5zTfEOOcuH5M29bxbUzYv/NoAVe1Izv+bFr/5E2K6LtBpCtP89M8pnaY8DXOX2OcUzGGdL5eVSdeOMTmxu+EUBnpT3b2+vdhjYg+RzQAo4XA55vzcVcnbh3fnl6T6E3wIa2PwF8XmtCI0CDR/778GzCGPP2C5P41E05tohnjjlBp+pqzj3WckafY4cZvfMoY/f3OfkaGbSsTfZ/4XO3J3spe8jpx6/g2/vD3yU6JZHg+Mq9fENGnRA8Zfz9OJ23O4lXlMs3l8VKVUUK3NvolbhxdrTqtQ5LMvwN+Cj8oNKjoT0Cn2uhwUKwq0nXqb8Sc0zA21s4IPweKqX8tNgApqhO3bV99hVkaajpzDS/2CPArI/PvMychewU8YXSt2AtQfNf/BmgDHeYSrHq383MYALM36AP/8kLapeAeoLqo8DuA8ANqR2R+0e+E1+bOpSnO8Hpaxaqig1BqLT8DOq3aJeWvdVkTaLMeDz4EKaoTt45vI68z+VWywikNSf+PnnIVzL6vauPq2tCX5EjQLbQLifo5bp+RtDak7JcBbT5LeoXwJ+fdVuH4+2jl+xGwsY6m3wd0IJwMwm+DnyKT36tgCEiRj3NbyjCi14O4ECieNvuxIJfqxK3j28hvJ36VtPAluAvcC7RQvwW7Aa9/A34x+BHoJrqEZDWH1zKSXgcbzd3P+byIzx7IvnA2p9HqdBKmOpmu1j2BJfseq7GfAruDncGlQLJ5YBhIkU5urZV8jkoZG73eifU65Oc3Bz58GI35t9hO42qgOr7NRHRF/h74yasAfeBQINoMSCboRB0Duo0WkLDyj2282Fy0kWT/FdgjZoDsEPA6kN0iB/GSHQhC+jECvRfKJoTkOhgGghw6ASONoYdi3QyHKdjMBtqkes99FGiTa+3boXbj2rE78m2VoK637cACoKtKk/K0DcxQ8Az41Au7qB3ncn2FVld4irRpdOq9DLSRWtHqKLQJRzmDf9M+DbTJYyT7sWAEUAxdxX1gPrD1pltJm6IdCbQWf6+07Ff+gUZxNB89iB+CTqjduDZGHV87TuFLBUoFSgVKBUoFSgVKBUoFSgVKBUoFSgVKBUoFSgVKBUoFSgVKBUoF2qjA/wG5AfnI6pQR+AAAAABJRU5ErkJggg==\" width=\"85.5\" height=\"18\" style=\"width: 85.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere are a number of ways to do \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003enumerical Integration\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = A(n,x1,x2) \r\n y = x;\r\nend","test_suite":"%%\r\n[n,x1,x2] = deal(1:10,pi,2*pi);\r\na_correct = [3.065357 5.25927 7.057977 8.618935 10.016842 11.294017 12.477158 13.584381 14.628646 15.619599];\r\nassert(all(abs(arrayfun(@(i) A(i,x1,x2),n)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(12,exp(1),exp(1.5));\r\na_correct = 9.752678;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(15,-2,10);\r\na_correct = 50.909769;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(25,-10*pi,0);\r\na_correct = -267.631308;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1000,0,1000);\r\na_correct = 61793.524569;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(10000,5,1234);\r\na_correct = 244011.112390;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(123456,10000,12345);\r\na_correct = 1644471.557504;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1:1000,-pi,20*exp(1));\r\na = arrayfun(@(i) A(i,x1,x2),n);\r\ns = round([sum(a) sum(diff(a,1)) sum(diff(a,2)) sum(diff(a,3))]);\r\ns_correct = [2087798 3114 -35 7];\r\nassert(isequal(s,s_correct))\r\n%%\r\n[n,x1,x2] = deal(randi(15),rand(),100*rand());\r\nt = 'sin(atan(';\r\na_correct = 0;\r\nfor i = 1:n\r\n a_correct = a_correct + integral(str2num(['@(x)' repmat('sin(atan(',1,i) 'x' repmat('))',1,i)]),x1,x2);\r\nend\r\na_correct = round(a_correct,6);\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\nfiletext = fileread('A.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-23T09:34:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-16T08:49:13.000Z","updated_at":"2023-04-23T09:34:40.000Z","published_at":"2023-04-16T17:57:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA trigonometric function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x) = \\\\sin(\\\\arctan(x))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in radians\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eApplying \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e recursively we define another function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)=\\\\underbrace{\\\\text{T}(\\\\text{T}(\\\\text{T}(...\\\\text{T}(x))))}\\\\\\\\_{\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\text{n times}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe then define \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the sum of value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n) = \\\\sum_{k=1}^{n} \\\\text{R}(x,k) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinally, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewe are asked to evaluate the integral of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, over the real range \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[x_1,x_2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=\\\\text{A}(n,x_1,x_2) = \\\\int^{x_2}_{x_1} \\\\text{S}(x,n)\\\\ \\\\mathrm{d}x}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1=\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2=2\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\\n a = 7.05797686912156]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=7.057977\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThere are a number of ways to do \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumerical Integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44694,"title":"Monte Carlo integration: area of a polygon","description":"The area of a polygon (or any plane shape) can be evaluated by \u003chttps://www.mathworks.com/matlabcentral/cody/problems/179 Monte Carlo integration\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle. \r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\u003e\u003e\r\n\r\n^\r\n\r\n*Steps:*\r\n\r\n# Define a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon. \r\n# By a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. _Other schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon)._\r\n# Determine \u003chttps://www.mathworks.com/matlabcentral/cody/problems/198 whether the sampled point is inside or outside the polygon\u003e. _Due to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null._ \r\n# Repeat steps 2–3 |N| times. \r\n# Based upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon. \r\n\r\nInputs to your function will be |N|, the number of points to sample, and |polygonX| \u0026 |polygonY|, which together constitute \u003chttps://www.mathworks.com/matlabcentral/cody/problems/194 an ordered list of polygon vertices\u003e. |N| will always be a positive integer. |polygonX| \u0026 |polygonY| will always describe a single, continuous outline; however, the polygon may be self-intersecting. \r\n\r\nFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\u003e\u003e\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\u003e\u003e\r\n\r\n^\r\n\r\nEXAMPLE\r\n\r\n % Input\r\n N = 1000\r\n polygonX = [1 0 -1 0]\r\n polygonY = [0 1 0 -1]\r\n % Output\r\n A = 2.036\r\n\r\nExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of |N| is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). \r\nOf course, if the code were run again then a slightly different value of |A| would probably be returned, such as |A|=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique. ","description_html":"\u003cp\u003eThe area of a polygon (or any plane shape) can be evaluated by \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/179\"\u003eMonte Carlo integration\u003c/a\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle.\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003e\u003cb\u003eSteps:\u003c/b\u003e\u003c/p\u003e\u003col\u003e\u003cli\u003eDefine a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/li\u003e\u003cli\u003eBy a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. \u003ci\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/i\u003e\u003c/li\u003e\u003cli\u003eDetermine \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/198\"\u003ewhether the sampled point is inside or outside the polygon\u003c/a\u003e. \u003ci\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/i\u003e\u003c/li\u003e\u003cli\u003eRepeat steps 2–3 \u003ctt\u003eN\u003c/tt\u003e times.\u003c/li\u003e\u003cli\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eInputs to your function will be \u003ctt\u003eN\u003c/tt\u003e, the number of points to sample, and \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e, which together constitute \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/194\"\u003ean ordered list of polygon vertices\u003c/a\u003e. \u003ctt\u003eN\u003c/tt\u003e will always be a positive integer. \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e will always describe a single, continuous outline; however, the polygon may be self-intersecting.\u003c/p\u003e\u003cp\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\"\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003eEXAMPLE\u003c/p\u003e\u003cpre\u003e % Input\r\n N = 1000\r\n polygonX = [1 0 -1 0]\r\n polygonY = [0 1 0 -1]\r\n % Output\r\n A = 2.036\u003c/pre\u003e\u003cp\u003eExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of \u003ctt\u003eN\u003c/tt\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). \r\nOf course, if the code were run again then a slightly different value of \u003ctt\u003eA\u003c/tt\u003e would probably be returned, such as \u003ctt\u003eA\u003c/tt\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/p\u003e","function_template":"function A = monteCarloArea(N, polygonX, polygonY)\r\n % Fun starts here\r\nend\r\n\r\n\r\n% Note: the Test Suite has been designed to account for variability in outputs. \r\n% Nevertheless, it is possible that on rare occasions a valid submission \r\n% might fail the Test Suite in one instance. \r\n% If your submission has narrowly failed only one of the test cases, \r\n% then please try resubmitting it, in case it was just due to 'bad luck'. ","test_suite":"%% No silly stuff\r\n% This Test Suite can be updated if inappropriate 'hacks' are discovered \r\n% in any submitted solutions, so your submission's status may therefore change over time. \r\n\r\n% BEGIN EDIT (2019-06-29). \r\n% Ensure only builtin functions will be called. \r\n! rm -v fileread.m\r\n! rm -v assert.m\r\n% END OF EDIT (2019-06-29). \r\n\r\nassessFunctionAbsence({'regexp', 'regexpi', 'str2num'}, 'FileName','monteCarloArea.m')\r\n\r\nRE = regexp(fileread('monteCarloArea.m'), '\\w+', 'match');\r\ntabooWords = {'ans', 'area', 'polyarea'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not do that in your code!' char([10 13]) ...\r\n 'Found: ' strjoin(RE(testResult)) '.' char([10 13]) ...\r\n 'Banned word.' char([10 13])];\r\nassert(~any( testResult ), msg)\r\n\r\n\r\n%% Unit square, in first quadrant\r\nNvec = 1 : 7 : 200;\r\npolygonX = [0 1 1 0];\r\npolygonY = [0 0 1 1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 1;\r\nassert( all(areaVec==area_correct) )\r\n\r\n%% 3×3 square, offset from origin, in all four quadrants\r\nNvec = 1 : 19 : 500;\r\npolygonX = [ 1 1 -2 -2];\r\npolygonY = [-1 2 2 -1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 9;\r\nassert( all(areaVec==area_correct) )\r\n\r\n\r\n%% Diamond, centred on origin, in all four quadrants: small N (1)\r\nN = 1;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_valid = [0 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants: small N (2)\r\nN = 2;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_valid = [0 2 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants: small N (3)\r\nN = 4;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_valid = [0:4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants: moderate N (1)\r\nN = 100;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants: moderate N (2)\r\nN = 1000;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants: moderate N (3)\r\nN = 10000;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants: large N\r\nN = 100000;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 7 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.0016 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.016 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants: moderate N (1)\r\nN = 100;\r\npolygonX = [ 1 -1 1 -1];\r\npolygonY = [-1 1 1 -1];\r\narea_exact = 2;\r\n\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants: moderate N (2)\r\nN = 10000;\r\nfor j = 1 : 10,\r\n rVec = 100 * rand(2);\r\n polygonX = [ 1 -1 1 -1] * rVec(1,1) + rVec(1,2);\r\n polygonY = [-1 1 1 -1] * rVec(2,1) + rVec(2,2);\r\n area_exact = 2 * rVec(1,1) * rVec(2,1);\r\n\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 12-cornered polygon of unit 'circumradius' centred on origin: moderate N\r\nN = 1000;\r\npoints = 12;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\npolygonX = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\npolygonY = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\narea_exact = polyarea(polygonX, polygonY);\r\n\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% P-cornered polygon of arbitrary 'circumradius', with centre offset from the origin: moderate N\r\nN = 1000;\r\nfor j = 1 : 10,\r\n points = randi([5 100]);\r\n centre = randi([2 100], [1 2]);\r\n circumradius = randi([2 100]);\r\n r = rand();\r\n polygonX = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n polygonY = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n area_exact = polyarea(polygonX, polygonY);\r\n\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 5-pointed star of unit 'circumradius' centred on origin: moderate N\r\nN = 1000;\r\npoints = 5;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\nx = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\ny = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\npolygonX = x([1:2:end, 2:2:end]);\r\npolygonY = y([1:2:end, 2:2:end]);\r\narea_exact = sqrt(650 - 290* sqrt(5))/4 * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n% http://mathworld.wolfram.com/Pentagram.html\r\n\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% 5-pointed star of arbitrary 'circumradius', with centre offset from the origin: moderate N\r\nN = 1000;\r\npoints = 5;\r\nfor j = 1 : 10,\r\n centre = randi([2 100], [1 2]);\r\n circumradius = randi([2 100]);\r\n r = rand();\r\n x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n polygonX = x([1:2:end, 2:2:end]);\r\n polygonY = y([1:2:end, 2:2:end]);\r\n area_exact = sqrt(650 - 290* sqrt(5))/4 * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n % http://mathworld.wolfram.com/Pentagram.html\r\n\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% P-pointed star of arbitrary 'circumradius', with centre offset from the origin: moderate N\r\nN = 1000;\r\nfor j = 1 : 20,\r\n points = 3 * randi([3 10]) - 1;\r\n centre = randi([2 100], [1 2]);\r\n circumradius = randi([2 30]);\r\n r = rand();\r\n x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n polygonX = x([1:3:end, 2:3:end, 3:3:end]);\r\n polygonY = y([1:3:end, 2:3:end, 3:3:end]);\r\n \r\n area_polyarea = polyarea(polygonX, polygonY); % Incorrect value\r\n warning('off', 'MATLAB:polyshape:repairedBySimplify')\r\n area_polyshapeArea1 = area( polyshape(polygonX, polygonY) ); % Incorrect value\r\n area_polyshapeArea2 = area( polyshape(polygonX, polygonY, 'Simplify',false) ); % Incorrect value\r\n \r\n % REFERENCE: http://web.sonoma.edu/users/w/wilsonst/papers/stars/a-p/default.html\r\n % Here: a {points/3} star\r\n k = 3;\r\n sideLength = circumradius * sind(180/points) * secd(180*(k-1)/points);\r\n apothem = circumradius * cosd(180*k/points);\r\n area_exact = points * sideLength * apothem; % Correct value\r\n fprintf('Area estimates from different methods: \\r\\npolyarea = %4.1f; polyshape.area = %4.1f or %4.1f; geometrical analysis = %4.1f\\r\\n', ...\r\n area_polyarea, area_polyshapeArea1, area_polyshapeArea2, area_exact);\r\n \r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2019-06-29T13:06:05.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2018-07-02T02:19:05.000Z","updated_at":"2025-09-14T14:22:43.000Z","published_at":"2018-07-02T08:55:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe area of a polygon (or any plane shape) can be evaluated by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/179\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMonte Carlo integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSteps:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefine a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/198\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ewhether the sampled point is inside or outside the polygon\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat steps 2–3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e times.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs to your function will be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of points to sample, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which together constitute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/194\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ean ordered list of polygon vertices\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always be a positive integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always describe a single, continuous outline; however, the polygon may be self-intersecting.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026amp; middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % Input\\n N = 1000\\n polygonX = [1 0 -1 0]\\n polygonY = [0 1 0 -1]\\n % Output\\n A = 2.036]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). Of course, if the code were run again then a slightly different value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e would probably be returned, such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" 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\"},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUAAAACWCAYAAACvgFEsAAA0/klEQVR42u1dB3wUxfffcne5Sy69kt5IJUB6CIQmvRNqaCJVQAQBRUEEAcVKVaQJigXsBQsIP3sXAbErCgoooNj/CneXm/+8u1nYLNfr5m6+n8/7QG53p7y38503u2/fMAwFBQUFBQUFBQUFBQUFBQUFBQUFRfPDbCx/YEFY4vxQ/14sB7Cw1BSy1Ucxlo+wvINlP5bO1EwUzQVfYnmdSCMhuvfJ32ewRGE55EcCPIzlOBbewfNPYTHIUM+utMvSNc7qwxd4ltwfuVjKsbQOEP1TBAH2if7/D7mRM8nfO2VAgCos6gC40T1FgM7qwxc46Mf7gxIghVvgbBCgcEwgwFuxHMHyE5be5Ng2LHpyfD45doocG06WRA8Qz2WkqC5bxwRMw/K7aHAtxfIf+XsxuV7cloXkuJGQ9zg7dVlr+yPEGz6HZQOWk0QHNS722Vq7orG8gWULWdqC511roy9SfQD6k/qgzR9iWYZF6YCuYrHswvI2lk2kHQOs3CPW6gBcLWrT06T/YtjqoxT29G5Nv67cF460ay5pw3tYNpPyz2L514r97ZW5RnQdjKUfiDffh/T9H2KPWEpL/oGUABkJAQ7Fkkz+/7GF4wvJwICbpZTczA+Sc54kxi+yc4yxUnec5O9e5EaRtkU609ury1LbAcJzzzZYssjg+VE08J3tsyUPJAJLPfk/T875zo7XItZHCSl/Nzk2hRy7yQFdXUf+HkT+7oClwYL+7dXB2Fkh2OujFLb0bku/zt4X9tpVS8p4i/y9iPy9xYb9HemrcN1gLGXk/zDukkQ2mUOpSJ4E2IL8bSDPB6XHs0W/XU9++5rMum9i+YzM4LaOOUqASVbaIr3R7dVlqe3CQNSL/v6VnFfkYp8tkRlPBhB4Cw9h+ZNcr3aQAOeT/68nx3qSvw84oKvR5JiReEzQdo0F/durwx4B2usj44TebenX2fvCXrsWSPrdzwoBZjvZV+G6BCLw/y/IsVHk75WUiuRJgHGim+tXOwPgBvLbZtFvcDzMzjFHCdBaW6Q3ur26rA3ePyTlWCNAR/tsicwmk/NvJH9/Rf7WOkiAgsdwnx0CtKYrWPJuJ8s6OG+dBf3bq8MeAdrrI+OE3m3p19n7wl67Fkj63d8KAcY52VfxdXHk/5+RYyPJ36spFTV/Aqwk3oU4ZOM1LBl2jrlLgEdJ2SzxXuzVZYsAHVkCO9pnabvEy6opxHs4Ixkwlq6xtAR+RfTMFJFy7ekKwpu6kv+Xk/N22FgCW6vDHgHa66MzS2Bb+nX2vrDXrvbMxYgIljxntEeAjvSVEqBMX4Q8SW4aMMBLIhKcIbop7yIPhuFGOk+eA4mPP48lXlTu5Yw5zGYfeW4z2sFjjIW6tzvQFuGBNyw9XsByt526bLX9D9HDeHjI/QmWdg5cZ60uS+3KJDf/EbK8OyHxOqTXSPUheCbwrOsx8q/wgsKerhrI+dvJg3d4eF9g4yWIpTos6UI6edrroyUCtKZ3a/p15b5wpF1zSRs+xfKo6Lg1+9srU3zdHVhWkP//SfrxPvn7W4bGUlL4GcJApAhOvYNTMF709yxCTpdTE1EEOm7GomPMbxzXUHUEpd454hXvIHJY9BiCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCQp4oyIgPgWSN8VQVsoY6IVzRHoSRX7ZoiqaIJ2Mqn6pCvuA6Fkc+/dCcgr8OripHNw5P/7FdXsQMqhYZjqb4kJbDOsR/8vqtbfUgQ2rjDyUkhORQzcgPNQURMxeNSP8RxtT2awr+6lAc+RTTNCM7hRxQmh0+59N1FTrDMx2RIAuGpUM6IZqqW2boXxW75/xTdRfsdO7JOtS3PGY31YzsELtoRMYx8Zg6vKb8fNvssNlUNTJDv8qYHWJDgbx/Z6kxIULRk2pHXpgzIPVzqa1m4d+oZuSFpAi+94d3lRmltupdFrODakdmqM6PWH32kdomhtowPQ+SS2ZT7cgLozolvisdVA0dE96hmpEdcrfMzD8rttOvD9eiqrxwmv5ehogcWBX76S8PmUnwjVvbGuqKIx6gapEfWqdrh946Nus3/dMdEcjy0Zm/tcoIH0w1Iz/gMbT9rRVtG2FMncFja0BVHCR7jaCakSfGpsWFoPrcaBSnVUBK9FCqEnlCq+H3tW8d1VhbEtUYGsK/QjUiW4TFRqj0dTUlKBWPLfz3GKoSmYJjmJ1larX+cG4uYi9u40chP2h4nv33zptboTuWFCP4P2N5dzcK/wO2zESTV+5GiVlFeo7j6PM/2Q4qlv13aUIC+r2wELVWq3WceeNmCvlhEMsy6Mj+7iaB/+PfBlK1yNCp4LhHEzIK9XO2HUQdh89GLMfDZEXjNmWIAeD1fYK9PyDAxZgIFSwLO8aFUNXIbVAxD7dtFakznB6IQNoUR+jwbw9RzcgOakx4/1c3bBYCApx054swUYH0p6qR3/J3e6uQEB2QH8jHOTmCsfpS7cgKIQqe/eeWhUVIIMDlC4qQQsH+jY+pqHpkBRg7aOIdL5gIECQutaUez2APUtXICyrs7f29KD4eCQQIUoAJERPjNqoeWQE+qUJfvtftAgHC/8lk1ZuqR1ZuxbbYlFy9QH4g7etnII7j6WQlM/SCAbQfe31iAlyACRETI2xZqKAqks3yd2tRfviF5a8ghXnhsLPaFqoh+TgVQHS1g6cjMQFeseJZYbKiHxjICJvzVCqdmPxA3s/OFozVnapIFlDgpe4fi68rQFICvOnaAlgG08lKPoAxg8bf8nQTAgSJTsqEyWoTVZFcBhX28ubHxSEpAYLkYGLE52ygapIFusGgOvxm10sI8JM3ugiT1WVUTbLAhqjEdJ2U/EBqBk5BHM//TicreaArDJx3sbdniQDnYWLEBHkWn8NTVfkd9+Vmh12y/BUkNysMJqv1VE1+B8/xirM1AyYjSwQ4dunjwmTVharK/7g328LyV5A3s7IEY3WiqvLvoFIq2LMLZuchawR4w6w8WAbTycr/gLGCie4xiwQIEhmfBpPVPVRVfh5U2Lv7dY6V5a8g6UolGGstVZdf0REG1f59na0S4Ed7OwuTVR1Vl1+xNiI2WWeN/ECq+l6Bl8EKSDZCcwP6ER1gwLyOvTxbBDgrNhYpWfY0PpelKvMb1mSkaqwufwVJx+fgc1dTdfkNHCa205V9xiNbBDh68SPCZNWeqsx/WJWKvTtb5AeyLzNTMFY7qjK/gMXL39PzZuQiewQ4d3ouUiq4U3Sy8htgjKBRix6ySYAg4TGJMFnR1Fj+GlR4+XtqJvbu7BHgb1iSFAow1l1UbX5BDQyqd1/uaJcA33mpozBZVVO1+QV3aaPidXO2HrBLgOU9x8Iy+CSdrPyDKhgoe7F3Z48AQabFxCAVy56gxvIL7kxOVOv0pwbaJUA4Jwmfi6+5g6rN904FJrQTZT1G2yU/kJELHxAmq0qqOt/j9gTs1f3mAPmBvJyRIRirnKrOt4NKpeJOXD052y75CTITn4uvOU4nK58DxgYasWCrQwR4zdaPUWhEDExWt1HV+RjYmzs+BXt1vztIgGexxPI8GOtWqj2fogwG1evPdXCYAF97toMwWZVS9fkUt2rCo3VAbI4QIEjby0biZbDyGFWdb9EWBsgL2KtzlABBJkZHwzL4KFWfT3FLXIxKp/t5gMMECOfCNfja5VR9vgMmsqNtug53mPxAhs3fLExWrakGfYdl4M2ddYL8QJ5LTxeM1Yqq0Eeeuor7/srxWQ6TnyBTL8+EZfD3VIM+QwmMjaHXbXSKAK+5/2OkDouAyepmqkLfLX+/uwJ7c787SYC/Yok0L4OXUC36BDDRoFeerHWaAPc8UStMVsVUjT7BEiAyIDRnCBCkdad6xCmU31AV+gZFMDCext6cswQIMjYqCpbBX1E1+gSLoyKVuvM/DXCaAM+dHIDgWlzGTVSNPlj+KpRflXQc7DT5gQyZu16YrAqpJr2PReDF/VJQ4BIBPpmWJhirgKrS68vfL68YleE0+QkyviEdlsFfUE16HTAWUP2ce10iwNlbPkIqTRjswngjVaX3l7+fj8ZenCvkB3IGE6eW48BYC6g2vT+oXni0xmUC3PVIjTBZ5VN1ehULgMCAyFwhQJDi9v2N2Iv8jKrSu4CBgB7DXpyrBAgyIjLSiIn0MFWnV3FDuFah/+9Ef5cJEK4NN+/vfD1Vp1eXv4eLavsZXSU/kEGz1wiTVQ7VqPcwH7y3My4ufwV5NDVVMFY2VanXlr+fjB6aanSV/AQZNSTViMs6RDXqNcAYQAOvXo3cIcBZmz9ASpUaJqtrqUq9t/w9OAx7b+6QH8gpTKCh5mXwPKpV7w2qpx+sRu4S4FMPVNHJyruYB8QFBOYOAYLkV/eCZfDHgaScSBm1JQsGwkPYe3OXAEEGR0QYlSy7X0b9U2IJdfFaSCCqlVFf5oZqeP0/P/Z3mwChDA0uC5c5R0b90zKuJ20NJbaWA0KBsPKrehrdJT+Q/jPugonKyMgrdMl5DivNDGuY1D3p8IZpeT/N6JP8RVWOdqYMOnKNmmUNP7u5/BXkgZQUwVhp/nZsOxRFPrFiXNbRtZNyf+xdFv1GrIZJcfBatiY/fPOiERnf3Tu15YnBNfHv5SRq/R7krVLyHw0bkOL28leQoQOSG5VK9gN/9ysvIaxNPdYx6Bp03i4vciPj4PfKyTGatD4VMW+AjW8Zm3UU2/wxxk9bS7aIUmf0LY95c/WknJ/mDU5DXTq3Q+68ABFkxLQFqKFjonHN5Nw/J/dIPlyaGzbWX7aqzo2YfVXf5C+AwyZ0SzpclqMd4dCFGg2TetPIjGOGZzoiQe6ZmnsqJy7Ur0kEsLf2/sDw8EZPkB/IT/n5KAQTKi76an/2q7YgYs0PW6obBV3/+0Qd6lMWs9eRa6tyw+cfXF12TrhW/3RHNLhd3IeMf5MIwIRi3Lm5EnmKAHdsqkAsa5qsUvzYL3ZIbdx+0LGg7/0ry85V5oQ79BilT3nM//57su7Ctcc2Vze2K4xY5Y+O9K2Ife2cqC1HNlWj+nGT3SK/Cbc8jlZOr0Bi3lg2KuvHKDWT6fPnL7GhlfdNa3la3JaFwzPgE9gWdi9uk6WdeXRzdZOO/N/jHVDLJPXfmDBO+EvwiDaGc5whWaE45ylRsKyRY5h//NmvQVWx58W6BoEJCOYie7YaURf/ovTa9VfmNoaouJ/VIdwJf4hSyf0CjyrSkjUoOyPMI5KKy4IyoWx/9Qt0umF6y0apvoe1j3/RgTGpvrkh85j02v6Vced5heqEj+Xk/CHpBmlbJo3s5hYB1o+biv7a2aFJmSe31aDkWPWfvu5jbovQv8GRELflu01VqFWWAyvZnETNyIOry43ii396oB0anhqNFick+EW6hoUhTFTwVQCEQ8z3oGyFgQVJVf3Vt1FlcUh6M84ekPI148BeCwMqY5+WXrtkdCZaNDcf3XpjkV+kRaIalbeN8ni5ZW2iTGX7q183Yp0uG5N1ia3wUvJpR57Rzh2U+s0l19Zmo8o+V/hUKnpfjmYOzrukH+OG93SLAIdOvhYd31rTpMxP11agNjWdfd7HsopydHp7uyZtwd56Y1a8ZpgjHmTIgKrY/X/saH9hSda/IqYxQ6nUvWFn7w1vSW1oqJ5nmOe94C2HY5Y5vzIpyS/9WpGYiOK0ysaN01temJEPrio7364gwqHdtgqS1J1WXJ51Srj22w2VxqK0UFTfr0Xjr9/08dgS1FE5frgn4jgWbV9f7vGyH7y3DPE8i376vJfP+/XL131MOi1OD0Xfb66+4BxgQvw5L1nTwaFHHfkR6w+tLj9/0VNvaYgODzF2HnUt8sQLCGdk4IhR6NDai6u8jbPL0Oh5d7tV5lXr30Zj+leYVotQJniDw/tWo6s3vu/Tvo1ZsgNFxCXr+lfFGgUvELisf2XsR848c43rURrzwNguif/rVRazI1TJlClZ9n94ydgIXstZH5LENy1bgvcHz3+88kAVE+uLHUNDDb4kvu/y8lBvrdaAl/WNuAlLitPCGkbWxb8wtnPC7qp87UJnnuHlpagvG1ob99zYzol7awsjb8c/9YKlYnKSWv/mrjqfEsX6O9sgvFxEv3/X1+Nln/22D8LLUHTfXW182ifQYUqSWkeW9r06YB2DrkHnOUlqZ/bF5WryI24EGw/vEP9CcWrYKPzbGnhemlPayTD9ntd9RhKQ72/YpFlowqg+aPyo/mjMtas9Uu7UlbvR8JFD0YSGnmh4wwg0be2rPu1Tu4FTEcvxjSzPf6BRMB16l8XsBA7r3iZqG9ZzrNsPgbHMwmRk6BQWZvgKE5MvyGJ1ixZAgHovhuSMB4I9gknJF/15MSMDQSZr2M8E193ZS31KUCnYPdgba7xpXj5yJhefO9KtUzzq0z3Ra+X37paIundO8ElfIIED6A50qODZ3Vin8V6y1QA8aH8Li4zVDb/+fp97g4EgU1ftRWmFVQZMUeAoLcGi8OZLlioVy/4QzfP6J9z8JM0R6YLJFntpe7zYnygg2HWYaL3ZD/h6ZWpMDIKXObg/T0K93n5raZqwOFZf1y5W/8Ohnl4ljNNf9YaXFGjL6lKv1bF5VampjjNf9/ZqX0BXdTWxetAd6NAHb9UTWZbfw7KsEZ5heSIkJVhk8DX3QD5CbCsetr3t6qs3zRF4EO+AFwhTYmKMpz0UmyeV77FXxuNlN65nojc7g+vY1w0TrbfI72BuLipVq/W4nnO4unE+jgooVyrZ7yMjlLpnH6r2GmkA8QE5ARF6k2QVChbdv8Z7JAs6Al2Bzhjf7h9jmrBYltMnZhXpJ96xixKczU/vPkSl3UaCx4fw5PGiFz10mxiHB/W/JWq1bn9OjseJY31yMnhMBk+s3+1gChDtUS8sg7ekpMBndwbsNUNapyI/xbCF8zyzGW6WSWMyjH8d6+dx4oClLyyBvb00vaxjPOrbPcnj5YJOQDegI6KrcD/ZqpLj+aPKEI2+75W3UbKzIFfc9hyKT8/XsRwHDsUUP8e9MvlKlj2sYVn9BkxYniSPnlqtQcGyr/mgDwnwQmKTB9t/Mj8fDY+MBO8VnmGuhVgwGXxNMwx7UH/n52r1h17v4vEXFPASxNsEeO8dbUx1/XbEcy9aQBdYJzrQDdbRUBnYKZzhuIfh3ils17dx5oZ3KfER6TV5OVKo1HjJqwCHQjaf3IVguQ2eb8HXGsc84En9iAlEaV7+TvNFBxQM83ZfD31p8mZWFspSqeBFx5+46EGMvJChUrIfqlScYeXyEo8QCIS9QIjKyc+8H6ICdUBdD93nmVAb0AHoQmX+1C5DZrYaxnH831EJabqxN+8MauKbce+bqGVFN5NDQd6eaxgZojsmrV9TFArdKw5uWG5r6UjCRBJ91PaZeJlqOIGJ19U2/0Zi+yBcCBPqO4z/vzO2wffMEvi8bGDvJIO7LxUG9WmBOtbG+Sw0pa5dLBrct4VbZUCfoe/kEzuvvzl0A5k8r3if4xUGU8zg1gNBR34NCx9E2ugEHZ4MwKEYzMgcCZgAXoHQkvlxcS7HDPbH3hgm03d92O4U8GC3YeJ1pb1ft2yJOoeFGTjzM8v5jOvZQnyJrnjZdzopUa1zZt9esfx5tB/SqHm0+pYSnxHgKuy1hWp4U92uXA99hT5D37EOujQDOynMJM0as9p0NExf93pQEN/F2D7OyPKKt2XsUFiNGdR3CA3Vf+lkzODJi4kKZvmy0ZhwPxwUEWF0ZZ8RCAvCHuSPuJhqpnkhTsGzLwkxg85uYARJD7AXhbwdZiMNU4E6H9tS6WpsnxH3Gd4cxjUzW3XleP60Whupr597b0CT35RVr6DUggo9a+aB5uJQXIIKTCrHYBMjZ9LYP2jO2AxLk1Qft3euMym3Tl+M7UPYOjsZeeVPdHbCmsLz7Pn21TH6Ywd7OEwqwwemoJqKGJ9/nlZdHo1GDEpx+PxvP+qOKkqj9LiPsnhz6M6ExfL8C/AsrLRbQ0DGDA6avRaFhIbrMNn/0AwdikvfaGFP0PRGC2IGTzlALvX+S1aaCcT7iANJVz/OyUGt1WodJr7/GN/H9nkLxbCTW1ioQv/opgq7pPL3D/2QNkyB7lhS7HMCvH1xsaluR5KuQl+gT9A3JjD2GTZNWCzHn0vIKNRPuH1XgMT2fXAhto/jOIgzjmACCKaYwTyVSv9udrbNdPUajgO31y97C2Di/WS4nbT7G5OToY16fO6nTOBtr6nheWYd3ISwp4etmEFIeQ9L0SP7u/ucAKFOqPuZ7dU2n09CH8wDyhSKpAkwWxVDOAiktO895ZbmHdu34lkUl9ZSh0n93wByKC71sDBpfARvW+FtqSVy2WHetxdu2iw/tfGGMExulr5uOXExtg/aB6/iQ5jARb1Cwf7VMjtMd+DVzhYJZsywNFOaKl+TnyClrSPR2OFpFo9Bm3Nx23Ef4M1hfQDbSU3uRRIz+E6zIz94u80rlAZM5rBTY8BvgWoOwcAkAm96pV9fjMTeF/Gs/IWWcDNJv3Pem5mJUpVKHYT54OM9mOBAulLBvqdUmmMG9acuEsy/J/qjqEglWr6gyG8EuGxBoakN/4q23oQ2QluhzbjtEEWQHiS2GgxhIpHxqTpICdUciG/6PW+g3LKujQxrSmJwW4A7FJfgMkwmZ5IVCt1uEjMIXleYebe2hf5sGG7Xl2PI5usQxgPhPBDWg3/fx/guLlFeExbLNPbrkWQQvvWFDc9hovjyvW5+I8Av3r3M1IYXd7S78K0wtBHaysg7ts9bSINwEUgJBeEjU1a+jOrHTEBDRoxAY69f59+3une/hOpHj0f1I0aicQvuQyMXbEPaqHgdxysgzVg3JkgRzzPMy5hcGoFkHjcvf0Hy/NyuxRGYiD/NzUWQK5Ck4/JFVhA5ozP2qE4lxofoXn2mPZowKgO1KozwG/kJUlwQgSaOzkAvP9YOxUar9NBG3NZOQWwnyCQ+S8FzhlFdU9E/JEHp4zdWomETZvqF/CaueBLNGFqKhASlD8wpQSmxaiPL85BmLIEJcoDBFkLSA0w64GV9K4M2tQYi1nIcfIv8c5APKDESeZ59BWIGw0J5dOOcfL8T4MJr8hC0BdqE27YnCD10i+jYKuoN8cZHINc0VJiyqPiaAIcP7Yd0TzdNwT+hWxJ4fkpqqYtoj8WICec3/G93Py/5lgEBYlKGZ5Gx1DRNAF7wStAPfP724yc9/UZ+EBANbSCrhruD3ENvgtGdE/ZJ9/3YMLscTb7rZZ8T4KSGbpfsQbJ6Ug44FvHUUqJJC27kutBQc9gCw9zJ+H7f1AyV+S11Y6VGA8kYzjAObE4UhFjXIlGtz8vRorgYFfJmnkFrAuEvUDe0ISlBDY8o1lKzXESH4sj10o2Bxg+u9su3xENGNqCzj9Q2acvIuoQD1EpNcQ9kUBE2Ldea4+y+JstRX2AK9j7/bRUSov8oJwfBBlDEs6ijpmkCXqFgz94wK88UhDxzcrYpHg9CYlz9NtcZ+eP7vqa6oE6oG9pw/ayWSKkwvZ2nk9VFhHVqFXVo142t0MHVFejqhkp0+Q3++XwONkwa1KcOvbK8DH28qhyN65L0W0l2WDdqItFzQEw+v86Ojb0QdnI4NxdVaDQ62LWN8e43wVE8wzzFkuQNZ0Txf2lKJWzFuZqapwlgQkAf7b0YG/jUA1XwAgIVtNSi/fs6e438oOz8XK2pLgjCFn7/8JVOwmTVgZqnCdaGR8fpR12/EV1139t+T2ww7uYdqKS2F+J4xRn6uOLS53/oVcm2m79gMhJCUDBBPofPifF0vbjcE7E8r3smPf2SwOerMSHj46epsZpgdXqqRiclJ/h+GJ7HQbJS2EfXkxsxQVlQJpQNdVj6Vjk9RQOT1SpqnovPajHRnIZ9gGWV2mrRdmGyqqEmuoiVEGRs7dOz5zMyULxCAdlWfibPCt32OLEsgfCby8LC9N9YyVYDwc/EWNXUROZBpVRwp+ZOz7VKVCQI2ZQe/8Sn7idIhTKgLChTGowtljnTchEJgaGTlRlAMCbCkVUA9NYDKCwqDiarO6mJyKDCxHZyRkyMzeQDsG1lT622UdhLl3E9PU6KkmXfhKSl8Dneb3YSnCYqFGCsO6iZTKiCQfXOSx1tktZ7uzui7IwwlBAXciFI2RWBYGsoA8qCMm2d+/aLdcJkVUnNZMKdQDRyTKBa1n0ULINP0MnKDLhh0R4HM0jfl5yM4Fti+KaYcf574f6Y+P5IVyr1r0mW29YE0l3h+o5TY5lwe1JCiM6aFyYW2LNj5ODUCy8rxJ+r2RM4V3i5AmU4sv8HtAnaxpg/qaLLX0wwQDRy/ARuxA33C5NVGTUVvmHjeV7nTObo97OzUZ5KpeNZ9h98/UgH6gjFy91NoPTLo6IajzuR9h42MifGKg12Q6lU3HEgJme8uG3rykyByuVto9BX79v/bA7OgXPhGrjWmbqumpQN+3scp0PKRCwmopFrpmdNeBRMVrcEvaWwd3VscnS00ynoIW0W5BdkzDGDD+F/w6xUUYK9xa/gG2NX0t0DMcNLElzO8iA3VVvQ9WvPOp86/7O3L0NtWkWicK0CPXivdVJ74J4y0zltSyJN1zhbD3yiRyarNkFuq1uAYIBo5JoIoU2XYXgZrPw+2PkPblS0C3tZrm5E9FBqKgrH5IaJ9AgZpGLM4hnmfLlGo4OwGlfruAITNC4/2I21LC5GpXP17e7/HW8aMwjxfMKxX7/pg4YOSIbP2dB1M1uaznX1bXFstAomq6XBbCggFiAYTxDV1JUvmz5lmz+xK5rY0AONvm6NR8odeu1GYbJqFcy2WhqFvatf3dyG8jNMbtUajR6THdz8EDMYo2CYZ4XYvl8cTHFvTSBEhhirOFgNhZeW30+9PNPtt7qQtCApIQRlpoWaXlyAwP/ht92P17pd/pRxmbAM/jaIxxQQiolg3CUpSLc/vF8t+j+SUAFkxZQyNGHpo+4vg+//2JT2Hrd1cTAvfy+knXJXIIB5VmwsfL9r5Fn2L0ys+p1O7ENir+xwc5quG4PUVJD1Gr20s51H4vq++7g7qq2KQeoQziTtq2PR9wd6eKRseOtMJqv8ILXVIpUmTO+JvULG3rQd7V5a2uQTNv3THdGQEcM94gUWtx+AOIXqs2DlP0h5dUniUXf25F2akIAw+UGojC7ZA3sTi6XB/4la/YmF4VqF/r8T/T1CUqe+7I369kg05e0Dgf8LeQbdFXiDDG3FbV4QlMtfhfLz4g4DjJ4gqFELt6J9y0svSWQwZMQwD21+tEaYrHKC0VY3gld1xs3lKcjneAlcY14Cw2dzsOMXfN72OOzWBmEsnqhDlKsw6DwLvKT8YnxDukcI6vmHayCLs06lZI/hoiuwVML/4Tc45ok6Lh+ZbsRlfh6snnr9nHs9sEHRh6ht1xGoR2k0Ov/UxbRad12RbUzJyDZMvOMFjyyxVepQmKxuCMbl72cNdjYfckTuT0kxZZGG5bSFZ3SwEdN/bdVq/YGcHLeXwVrzMvj6IDNVvulF1SPukRO82LhqUrawQRHsEhguqiOc/GY6x9WXIGKSJZNVbpDZagEQirvL3wm3P4/iMwp0LMf9p1Fx8/tXxe6bOzD1q4ndkz7ITwldhL3ML5UhGn3fabe5TYKFtX2NuLxPgo3/4MZE7jyj+8m8QZFpQGFvD3Yxs7bjVyFeun4Gu7htSk52iwShPky0h4LMVte7u/yF1PUlRRE6nmft7fg1Ds5pjc+Fa9wh27BQHiar+UG2/D1cVNvPreVv7ynLkUKl1uOybO14qGE4DtKPwUZMxpkb3nW5voFXrxImq+xgstV1oZiQTrm4NH0rKwvlqFQ6Bcv+xTi245ewc5YRdnU74UQgtFgeNm/YHlTGwkvJQ6OGpBpdJSP4fhcvoQ0qJQ9f7mQ6UGUmPnc/XAPXulpvQ30qLIMPBtGYgudomFBWu0REsJtcQbu+zu54WA8bMUUlpOvGLn3MpXqv3vQBEC5sgzsnaCyFPbIDQyIijK686IDvd/H1BgXDvMc4v+PXQPgULkup1L3h4KdwFvYs1geRseBTQ1O6K2cJ6Jev+6DBfVvASw4YUEsY5zYoEjZiMtb3a9EIZTlb/5PbqoTtVTOCxFbzYH9g2Fzc6QwtCx9E2ugE2KDIlR0P03le8S6+1gDbW7ry7XFeZXcjr1B+GCz8BzekcTv2ppwhn+/y8lAvrdYgSobg6o5fibC7G7wthhjBs06S4MDwcHgbHCzGmqNR84a/f3Au0embu+pQSpJap1SysO/DZW7U3w3KgLKgTGfaAG1Wh3DgWVwTDIbCBLI/v6qn0dlP0mD3OJbjjJjE9jKu76dimrAYPKay23YyTF/3ulME2G/a7cJklRYMtpodgj24n5xYhr6QkYESFApY8kK6o84eaAMkNpjFMYwBdn37yko6LEuyNSUlaIyFyeeDoQOSGx0lnfM/DUA3zcs3bVCk4NmXGc/s+RCPy9oNZULZUIej7RnSP7kR9+H9IBhTsBIy9ptxp+NfeKzai9IKKg0sy3lyx8NO2BM8FRoRqxt+/RbHl8Eb30O8QgWT1VXBsPx9b0B4eKOjb14hjIU1v+h4Al8e6eHmVKlY9odontc7Go8IxA0EHgTGSoYl6I5NFQ5vUFRXE6vHRKVjPL+FqHnC4lg91AF1OdKmR3HbyRI8OcBtdTWvVBmASBwhnMHXrDN9hcHxymOM59OHRbI8/wTLssbSbg3I0TfSOaVdGrEX+xYT8IMKz1T3O5CU4GBuLoLwFbxUPcfYfnPoLiIwue6AZ12QXOG0Ay9m+mACx0Qe6Ma6Cl5EiL/ZtSawKVJkhCm2D76X9maKo3KoA+pyZCMmaDv0AV83I7CXv4p3csu6NjoS21fabSQJReIg7CjCi80ax3L8uYSMIv3EO3Y59PYZz3PQtqRAttV0yOVn7y3sFkyQoRxnwOd+ga8p9FHbIGbw3xK1WrffTszgxuRk0yd3gWwsvHR8a0CvJJvL37+O9UOjh6aaQ5F4m6FInoSG1IUmjckwQhtstbF/z6RGpYJ9M4DHVAsgjj5Tb7VJMFeseBbFp+fpMCnZC0XyJIo4hfILZYjG0OfKFTbbN2P9W5AkFZ7vTwlYSylY9o1eWq3V5e9Jc2yf6VU8Z97mUO3jJuZjz+6whmX1G2zEDP6A2wkZpQPYWAnwiZqt1FWHXu8CW1LqFQpTKNJQP7RxKNSdn6vVQVtspdiCvkCfAtRWVwJx2Nr0CN7O4uWlAV6UMM4nEXYXeAxfiBlstBUzmFnS3sDyin1MwA4qhmm8zwqxQFhKljm27w987iA/thPin24DD28gXuoey8uz2N5uWq0BtzVQjTUFk0vj2W/7WI/tU3KNeDn6AePfMJMMaIOtmEFItQV9wedODsjlL694LbtNncXl7/R73kAty7s1MiwrhCIp/djUQeaYwTTd2Jt3WiTAHhMW48nK9Hw9JhBtNQm8JimhQBjK4oQEk0elYBh4rpYqk/Z2x97gLykKhc5Suv51LVpAItaANBYmjH29uiYYpGRy5uveCC+LDcSjggGlkENzGXPMYCO0DdoobXePLgkG3Ke9ATim4iH0pNekpZeQycgF2yC2T4+9QwhFkssevGmYsN8Bj9VSzCCEz0BIDj5vfCAuf1/pGhZmEJPI1y1bok74N0Ik8OZQbhtbJ0C7OZJX8KwkLpEzPwcMNGPFcBxr2LyqtAmJQCZo2HNDYd55rYsM290Ft+00tPH155pmrd60qi3iAtOzmMjxfOOMe9+8NLaP5Rox2eyR4dIfNjObD55eenG1YerqfU1IMK2wCi+D+ZcCjf+igeTWYK9JIJAn09IQhJ+oWPZHxrzbmFwhxAzq24eG6r8UxQxCDCG2ZqAZ63KeY41CeipRbJ+R59kX8PE4Gbc9TsGzL0JbxTGD0BfoE+O7h/++uTExwWW0qjEI5DFl5R6Ukl+m93Bsn7dQzfHKH9XaSH393IvZa7qNWwjkDaFUkYFkq3HgLcHWlqdFe3lg8tjJePdVvCdRgZfExyJ5XickcViZlAReYEAZCwikc/s40/L324+6o4rSKD0mPghFmsI0j53xoI1ToM3QdugD9KVTbawB/7YrkJwK8KK6j19kzq03azUKCdXqyD4b5c2kD5HYg30cuABiBiFM58o1+4AAgR9GBYKRwrMTNaOiwxSHajQaw8c5OQjCTDDx/ddMZ+NwsgGTicQ/zc1FPMsYU2NVD8dpFZ2aua0y85M180OUnH7dba3RIxsrUFioQq9ScZbSjDUHFEPboQ/Ql7UrWiPoG/SRcSwpg3zdXHyv4XvuEY7njJPvfhmVdKoXYvs2M03TjDUfB4nj/0vIKNRPuH0XSsop0UdrVR8Dd+Bj2uZppLiQvFGdEj/7cn0l+nZDFRpfl4hiQng99qK+YZr/rl1TMBGeq2oRZlg5IQed3FaDdi9u9V+n4qjnGPk9x7SL2oLwOXdekf3zCdyPfctaox5VsYixnLevuSEC9+ER6Av06dXlbdDxrTXo9suzf2qXHzG7GfaH69QqateeJSX/wT1354RcVJiTbGA5Djz0Sc18TJViEjwSERGmH3NZuokzvri3Eo3skPBZfHxI88vr2LcyZrc4kyzsJdC9bfRJxrE0O80BHW4Zk6UXpwo/tLr8fJss7cxm1o+oG4alHxX34+jmalSQGvpEoKwVC9NCn/phS02TtO7X1ad934wev5jQNjNs9uF1FTpxP5aOzoJHMO0CxFTqHqXRJ8X9O/dkHepTEdP8nrPP6JtySLqXwJyBqUeayXMku8hLUY/7dF3FJfsldG0T/VBz6odGwXTAnpFe2o+B1bHPBAoBDsJ9kfbvlZtb63Hfa5tTPy7D95a0H4fXVCCyVAwEsPMGpR2R9nFGn+Tml4S4vibuVWlHGjomBExmDpWKKdo2K/93cf+Oba5uLM0KbW47xyXcNi6ryaz768O1qCYvYm2g2Kp9YcQ9Zx+pbXIvLhudeYKR9xvtS1CWrV38w/3VRnE/Ns/I+y0kJHD2qRnVMeEDKW8Mbhf3v+bnISVrOswZmHLsn8c7oP+wG3vzqIzjJZnhA5kAQl1R1LZ9y9r8A0Y6sqGqsXub6LeBG5vdWr4o4u6nbyj+Ax5THN9aY+xXEftxc1se2kFk/8rYA/CME/r4xPziP9oXRt7RDPsR0qNt9DvfbaxqNHmxS0v+6VAcuSWQxlSbDG39stEZJ4Az/n6sA5o9IOVoboqmeS7xW0SpM+oKI5a2L4q8NTkuJCB3U2uVET64c0nUqrIsLWQcUTbXfhSmh3TvUhJ1d3luOGS7Dg1AU4VW5oTPgz4Wpqu7NeN+qOBeg3uuKC10YCCOqYxYVWEd5gzgjmiN01nfKSgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgofIlrsEAqpiiqCmorClmjBAvsN3JlsCqgNxZIvf0EkXexxLpZZoUfBlUvUie1lbxtFQx2kgL2z7gTC+Q0nItlOyEeueBIMBMg4BxRQC65OWGznAIse4nhnmXM+318heVmLL8y5j00VjDmjZDisUCC1NssDKq+WBYQ40NZK8mxJVgOSNqxAQvsVHYTlq+x9LDQjtvI9ZAR+CiWPuTaFeT3eYx5O05xnYC2FtovbguycM3touPHsFyH5QXSDrnYappEPyorfbVnq9EW+m/NVo7YCdqx1IKtxHZSWrg/7NnpgIVr5GgnMSBpK2xkHkb+LsJShqUlltewXI9lH7GNJZ3lYYEMTDdgeYqUIdbBRiwfYvmc6PQlUr4lmzCi8QD3wa1Ez1daOV9ad18Hx5ajfZMNAT5Lbp4V5LetWL7AMpPcTJBZ5A1y7ARRWC8yqBjSSUsEmE8GzD3k3GpyLAdLsgXvwEiMCLPk6xbacQW5PhHLY1jus+BZSOuEGfgBC+2vELWli4VrhOMp5MaA4+3JbyEysZVUPyVW+mrPVtU2+i+1lSN2KhFdL7aV1AOU2uohO3ZKtnFPyclOYkBG7u8t/L6FkITghS2xorP7GfNWswJ5WtLbMCx/MubU8wusjGGx1wn3yJvk/yeJni2dL63b0bHlaN9k5QGCe34WSzRRxgfkOKSx2SVSmNDJy4gnwJBjlgjwUSzbsHQiv3WwseSyNrDE7egpun4nUTQj+p0ny0NxnWqJwaUDy1I71ZLju7HchaWG/KaVia2ekegn1kpf7dnqJTv9d9ZOsZLrBVuJ7aS0oPedduzE2Lmn5GInWx5ga8a8P4stkhDrTExCBVb0BlsenMHyIOk7Y8UmYgIU6v5RRIDS86V1Ozq2HO2bbJ4rPU6I7yhxdUEBB4kLuxBLKVnurBC5zNGkc3PIsX1EIcKDdXCXp5Nly3LRQIN/x1ohwEbiSn9FllZFknbMIdcPJOW+R9qRRW6AdVjWS+rsTtx0afuvEbVluoVrhOPDscCmQq+S8xAZyHKw1ZfEuxD0w1rpqz1bvWij/2NdsBMrul5sqzKRnVpZ0Pu1duzE2Lin5GInS88A7yKkBf1bRchQvEz8H1kmWtJZjWgZeqsVHYC97ib9Z0Qem9Qm4iXw54ScfycemaXz8yV1T3dwbDnat+jm8pwwXzSbnsYywksPyA3NuP3BYitqJ4qgsxnM8vcS5n+GeA+exgriWXRppu0PFltRO1FQm1FQUFBQUFBQUFBQUFBQNA/AWxpnd2qHfUvvcqGuKYz5NXigoRxLQoDYyBN2k7udvW0vX9jX27r3tA3lpnMTIMJ7lQPGgeBKiN2ZR35LdXFwFUiUKpTtjRvKWrnifrhahhQQ3rBWBjYS989VG9mym1h3tvRTYGfweMI+7tw/3rSXJ+3rSv/s6d7X5chR5xcAsTtTyf/BCLcw5gh7iAWCTaYhGn8GGUgQFQ5xZ93I4IJ4sQUWOgXBqBCcC/FDlRaU+iyZXTZjGSMapFdJyrRUjnAObFa+iDG/aboaSwZjjq3SSryfqyy0U9yPTNJniEuaLSn/C1HbILbwDnJ8kuQ8YeP0u0l5/rSRuH/jbdgI2g8R/hDTtZJcAzGfCiyzCAGBrfZIBoNYd4KOp5DzphGbcqLzpfq15J1KbeSofW4UlSO1j/Re2c+YP4tbQ871pr3cse8gSTvF97E1e0n1XyQiLmv6t2QzqQ4FG7IWxhl4c/eTciCOb6AN/YvvP7no/AKgsUNEXt1qxhxkCh2OIf8XPAmpByh8vvKYpMxM0umZpMNSAhS+G1wuIUBpmZbKgXM2kv/Dp00QlH0rmSnFga5Cmy21U9yPlWSAAFncIyk/R9S2lcToAAgcTpO0AwCBnp39bCOpB2jNRuJjL4nskSPRz04bHqBQp9SmnUXnS/XLWFhBSNvpqH1CROVI7cNKzp1OzitlLn4H6y17uWPfiZJ2WrqPpfaS6v9KEQFa078lm0l1WCgqRzrOVovO3WVD/9L7Ty46v4AGMssIeJKwOhhlE5YkkRHKyY3JSW7gnZIy4esLCIhMlCjdEQIUl2mpHEvLuheJB8RbIUBpO8X9AMO1J793sjAwxQRYRv6/lxCgtB2LyeD1p43E/Uu3YSNLellC7APR/PPJb89JCNDSPWCPAMX6tUaA4rY4ah9GQoBi+7CScxPIvbQDS1cv28sd+0rbaes+FuxljwAt6d8aAYp1WChZAovH2RoLBGhL/ztlpvMLAJf2ZtHfwrICDPGWaLmyhxjmQaKUEeQ3cLc/FClDcOPXEbaHT5EiLbjeMCNvId4L/B1tocxlFsoRzskQlXkdOZeRLLH2kJtB2s4EUT+yiHs+kdyI4vJHidoG591GyptkpR2bGO98cO+MjaJF/fvSho2E9peRY/Dv80QPoYw5w0cDOVZC7AbHs0W6E+psRx5rTCU25UXnl0j0y1hor9TuvR20j7icMol9GMm5c8k9ByuJPC/byx37StspvY8t2atAov9p5JjWgv6kj6LENpPe41NE5UjHWSFZAoNn+YqFaxkrHCEXnTfBdOItNFf0IF6LP9GW8e5nP3K2kacflgeCvXxpX1f078o14nGWRCZKhjyvbY46bwJlMyW/xcRDDAb9ydVGUk+hOUAZQG1yRf/OXiMdZ+DNrSIe65AA5xgKCgoKCgoKCgoKCgoKCgoKCgoKGeH/AS8924+Oc1GZAAAAAElFTkSuQmCC\"}]}"},{"id":60749,"title":"Compute the dispersion coefficient","description":"A contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\r\nG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \r\n\r\nwhere is the width of the stream, is the transverse mixing coefficient, and is the deviation of the velocity profile from the cross-sectional average velocity\r\n\r\nWrite a function that takes a (normalized) velocity profile specified at several points and computes the quantity \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.5px; transform-origin: 407px 187.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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RGAYu7i4LwTwFPTWudeTjNZMQem1zSZ2572UdANKqZrQVERzwWboe3gC1kZ8XUMHMOB6S3LCLfWYVjR5NLafHGj1QAAjWFPqWbOHIuR+V7XGutaMuw7Bx/rcBJGtb2zkj+ZAQntwLYGI+fXRbtu0+/3Vx8n7182sHHrAmHBThPRbBsyTXZrz+Hg/OE6UUsVKxmHFsp95cljT/sJa4/ckoqr/nTWCpvzcSgi/RP/+BTz6BLA5nLmWBXaBPoT/z5XCPmJNxC0TEPAcgTU3a5/uEesM69Ma5iTC5DDHLXlIyAWbodPrCVi5ZzWzsTax739I8xa0acdtuPQJufp93szd5ILBJIk1BCyntq6xYRZng8cdgzm8njWLe5/WcxjxrpomPzEHCrJykYhiqPsr5/EhC3H1vUBN7Mzjh91keWtWfX+xyzAvc/hpOuDAPYE3xYEQa0yvAG4iYjAhpJbEUY65sWmSpy6wNe63hTm2764T5dhnlnKfJxlNDkyf8NKWLAYfTJ084zO0LXlwzAWbIbDWv/u2zWbIM+e61nyiCOH6QQHzMBms0E7Zq4ZkfEoxQft38ge8pnGgAROmN5Vpb++LOZS915uzMR+jYSHsm9a4x6ovU50dXNq+pfuqqXpI1Evu48PaS4gXh4SmQ1QKO9sfxOqZ425WkQAfrxyFa+atSwP2GoUvL8eDUc85VULRxxRx8Vxf2ELPDQE8Duic2LKmCdVP7X4j5i37Np9xSFz7rpywGfJOdd7HnSp/aFOmqCHPnOtav0fVN01/6Bpq9UghYdXfqU0TZ1PGP+iLOexb+ZYfrn5Y/g7BDcWG/bSLmW9ClL453HmymVkr2aubUqoaVsS99x1G2qxJaMfwa1gPRjZDhuCygIRJveTPqL8bi6mvm7zW+GyeOCRhAcMvjp/bY+cPJ22ZHs2a1cUe92bqujKCdkzbk8WsSwD79JO+U3+S4YEsJNTuKey+uT7QeO68COTClvUfUH3hQ6Yhbg+S1lBNaAp6uWAz9B18BqzcLTu2R5H8xydFYLNFE0U5oA21eowJQ0KwnVqZGSFnmYBDYBE5AlfGBBYmXHyMjBliFgcFWMnX7cixb3NoZlDIsD4uO8XXbRyIlEQ5/vDosUMLRNBCJDLfKKRHQlGfr78jrp5sXZi/OZTATF9zfBzAsYghAO/ashb8Ya3J4uMP8X1WPrN6eZlJzDUELYhxe/J4dwlg7weqd8qJB3WdTY3TW91ePvSjt+uDhDUWuXXuy4Ut6xnOXhO6sfq8YHkesXCWrlywGboyEGpn6U2bYO4O7X/I9U2bnfny2KNgn6KVDTWj29yh7aUm4iC8B8sgm7z1h1kTBcVrvwgCriV0z7RdOyRy4OmKzbXD0bM0pMmw8spSk4XHK02pPn3TWE1gY+UkWxzhj3aYYP/nPZ7uyF7+8GPf4lrjAx++fdYE5RwJA+Pw4q0HPtTWW3r9OvTm6b6iJPVDIRUBOZSQe+BaObzbBLDXKBhIvVNOBPg1HqOj5ES0iYoh2yiAmbwXD9lVFrgW8xBa4dSWC1vWzEM+DzUfHhsGv8OnxcaWuvlMxYX7c8Fm6Lv4yk1L4jV0nG3mPr43NDJiNgmZadtUu/qzZ/9zQ977tvu81ojCwg9aKuEnZsJnX0UYY26+0D3IzP7EsXfFHrPOj1em7fvc/X7Omhj+3m2YmlTFNHr8wFgXwISxMX4z3yJsYPqzv3kLqCXTsHDQtcbn58pkS10A+1TLTdYBL+sQpvi/yYXR1rwywFxA5ML3e3STq7ZNAPuHtJmh/KmAgsSYInKoGjL0Q577+m0WwP7D6jPNzImzaULGwr5cGY2QVTALopmwoXAix3KDFkJVmbYkC5sYay7YDHmXegnCoZrjkL6mXuv3KFMQsHigGKCV4QclCYaZAr9KTaOwXFNKC7JGiHsdUvjA5px1SJ5p1hxsYSMrgS9CGAHmBZYpPAiJtthj09TwYdYTZHgOSz1pijGPsQTYYYQc18Sq8m9b/WtM5cS93kV9pwhbqkP50FMOHbSrapNpVhRbP2uNL0UAe3YzGR196JlnRnMAsf2FueNQAj74vH3zAp3DCtYH4okb6zi3CeCU8AlPV2cALHqc20OYcVM/wrh/PQTqm3XqyXrTI/YLHo2DMAs2X06q+NbY1BC2bD6czPkgyFwDY3SuVJS5YDMU63rhlZwJWGZhMK3kMg3zYBNls8PKg+kPLR6hjGkWqw/KQkqDtUpID7GgqexlH5OMMkIcLhaYvmYaMEk/2qozYe4lmxL+4/pm7t2FPgkEhxS+CQ6kZK56qwoYTN4kwwCbtm/Ax9Xz7XAt4Ucphxe+Mw46RgbLYXxtGrC3pLxHD+4fUrM17gTiejm8EUsOlsg5DlWn677SNLdovBz+MNtj9vZWgz3XNwngOmu0K7m+P+VDcMFEwYkzCFl9n1z5f/cLd60MWKDoT7CYkPh4+GDYcDDzefYl2i+NE7mRSOaYiVywGfpunv06JHPU0H42cb3NK2uP2uOkUSTWG60E0g+/gwyE1oKWwj7GQSy1WYINBFWqYuG1clwejCFlL4QJ/TI9JLQxziFRoemzrhGovvnwFyyWmKn5BtDSEAYcpDiYErf7Ng1fwjzc9w2YZQkuAIeZlEp3pphBPDJfaw7jaxPA4Gjxu/w3aUtxXXBIwQqAfxuhy1pif7lEs1x1pRU1EzxzQWxx66HPC2CAQ8oz0eS/ZBOhscBPU4nP4NBwMTHcTc0YvJg1UnZxDSct6Nwpp6XUDyKuywsBv1mnMCvnGr3lxcXfy/pj88FUZpuL5WHFFMepnI9p0ylU6++WCzZDMfeZ75bKlz10jHa9zSt7EXsNDNO/VYHn18S51Q1GHkoRhn48mLRZTyRQSMn6Z4fBj6jw6RNw9AVXAf/g52rELD8OhBmHC8bSlJObfRwTM5oWfAc0aYQmVh58kGDEYQDBjauINIkplkoOORC+cN0guFMa3xn3HOUETw7j6xLAKJ28K4Q5cOSghoClAAmHN6wncJzq66wNDzPB9x7C+jJhpQAe1+wmAn6zLq0E4dwzVio23vWUc1WruefPP5/NlBSSuDPQfroaZmtMtWidqaZutFM02zarDAIasiuCgFzTQw8RY7FCNqDBEh7lGdtdz4MBjcaIiXyItWHMGIeOr0sAj+m/6x6UWA5CPpVl4/UhgDcN/fDnETeIpcAHhg9/yvJ3+M16qeIGy7/luB5Lxcb76iBVogXsemOPxBdIeke00DbNES0KLZz8yDCwUxraIsIVEzfxsvWW2ndKX0OvIXcxGiFxzHWTd9OzOCigKVJxCRPu3AeFoeNbSgCTS5tDCFYNz3QPATx0Bc5wvZUYPEh9VvitIAWl1h29ibLNuR9yQFvDxArzDrMRp1HCKTb9QfjNeqniBjNMySyPLBEb1iYbB9qbD+eaBaDCHoogxAeIZQOzbv2wbGxZWPcQlVLIfZ6x3aQtW58IaYhXKSbjTcHaN7amgwK+ziHvP2WsQ8dHX0sI4MEWgNCApyyD8ffCaLR4vjGFsX2IAKMgCw3+H/z1VPRAUOPT4BRG2jvi9Dhlp5AoUt7Kb9YpsXEpz9yWa0rFxhPH4HBQFabP5Lotc5b6HnxXJnwRxoTw4G9N0ZB9H3y/MGmJB/4H9we0SNIlEjr3yYr1jDbFYYgkDnM1ZAAkKVjPfMsIEfYSOAB+bG39cz/cIczvdQsBhweeDRFubJs6Put3DgFMcg/2cngGzBHx5zCpSVaSpPCEAB67LKbd15UzNOXJdQHcpoHiX4JdCTsT8saeYtApHbVc4/MFr1kBacIrzHZrqdh4Bm/OCThmm7jEB/vwS+LI+a5g3uMnTXEjIeAg9EDYgjTmG8QyBDqM5aUIrJ6hDMkI4hghXNdU7OnBhT2Gd3+TFqO3y4kRJlQMoeSThiTCfM1lU8dnD7LSoOQFr+fRHjomrkfwQtIiTprQN6yOHFoGRQGFAB4D/fR7fL7dvtRmTb1ZlhoWQVeieeYXTZiFQWPBNIUxDH0jv1mvmYBj6LiXuL5UbPyayjkBxxJz2NcH4T0wo2E7w/iFcZyipeInhpiDgG1qbYUU+sYz5e9WXpCoFuKeea9USxmpPoksgDnc1CCNtcU1p455yvjoA8zJ9YyJnKIYhGKRl/mdHUlIUsZG8hTmkVBchC7+/5SY7z3PDgGcAvXmrzGSzthk997H2Jdo3p/UeBMfqD/2zfxm3VS6a+xzt+G+UrGx2MUlC1Zsw3zHOwQCoxEIATwautE3Wko5CC9jYi19hhoG0aeteJ8k12/CvGib9Zg8u6OBK+TGUrGxpAtDS/cVMi0xzEAgPwRCAC8/J95HOKY2bVud5q438RnL6vlOxyBgqdbGEMjG9FfSPSVi4w91fRaVkuYixhoIZI1ACODlp8eSNMCotLqhMJchMzxaA7ghNBAfSExdvbXVae56E0vbxzVjzd72fL9Zb0KbXn4G5uuxVGx87eIxh8L5EI0nBwJbjEAI4OUnt15n81MaLkRg+QXq1Icl3bYRmqmQkacSoDYpgH3u5bUKMCw/a2k9loqNLwOacwGGtFmIqwKBQhAIAbzsRHl/LNojfmCSohNPSP5i28APaRHAPnyJkacyqH05sKk+PqPzU1Q8NYHIsiiv11up2FhloalrYz3ko+dAoEAEQgAvO2kILYhXBO4TcI8Zmma5Vr15uSm212sqqabkeom5McQvj5IxuLv8v1SQIdGABaOzzqDpf3RZuBfvrVRsjFXf5v9l/u6sIWzEvlI4nly/JJJIiX1dfCKiw0CgBARCAC87SxaicoXG5CKAyTpjVVPMvNwmXI1hy6hTBamPS+U+tGHqoyZlammAx8bYZv62AuAE9XOwoOHPJlsO1UEGx8otO0WTeisRGxImHKvJCZoY9ZZmkYpCD1PBSypAhDUHKuI8QwhPWjZx864iEAJ42Zk3TYNYS/I0s+FZ0Ls3LzcJVx++xKhTyTJU5niNvubUQH9PMmoyf1staQLzCXwnQxDNNHcSFhAEn5Ird9mZmd5bqdgYAeu7W1wKpBgkuT4p9nxSBXgFpEAlKUVq8YHpKMcTAoEtQiAE8HKTSeYU/L4IYQRwfePy5uUmTcSHL6UmSyDtHflZMXfT0EhTi4s3IWMhUGzah1dCFnOkb/YOFIKgfNuV+kc7XNyqJpiXQ3/+nkrFxlj5EACxUFxag8oIfHXCnd0HY39qtqP5Zyd6CAQyRCAE8HKT4k3BTb42My+3VaLxNWbfoSkmyRvb1fAjk6sZAYgG8+ABdUqbnmsmdJL1UyOVg4BvCOVTRKReS5Z1hubLTypxbLmZ2UxPpWJj667JpeC1+jo72vKRwzGgcAMp/qIFAoHAAARCAA8Aa+KlRrDiMfhDz3DPS8mO5UOJUuJvb6G5XQ/WzRENZmqRbDOht2XfMh8ozG4Y3r4ZEzvVdD4R7sVvLxEbz8pvIv15q8sdtfCAAWuMfQ6GwYZffLlFh9uAQAjg5WbRhBPaI5mp8Mdaa8qOhUZFDVBKgnmiDPf0pZ/cT0ROUG0TzQShBylqLPGKPs2Efqiaz89rgM6EbNP4uoTzcrMwT0+lYmOsfDRdDnh1i4oJWcqu4TLxc94lnOdBOZ4aCGwZAiGAl5nQvvKD9fhRfKcUOThGGdI+/SQjrmsj9hZk1EJAct/tRQRfLOXA3j1R+PJ88+9SQu1Ix9xu0nKbBLBpiE3a8TKzMF8vpWJjVhnKz+E2qJfA6xLAfk23rcf5EI8nBwJbgEAI4GUm0ROsmnygPoH/czTOklJXF+rwuAdmNJseDVIV/08JNIQuG+WBGiZymJqcjxeRkyrt9/KBr0gML9rOWSJythPc1BLG9N3Fet12E3Sp2BygdUtPc2FgVteW+bxfTbttssyECXrghxSXBwJ9CIQA7kNoM383AdsW34vwhJh1QxE5WUQQnpeoICaG9j4ism/HUGAjn69EK4otnCsiV40Yujd1e6IXrGeEOaSrrnrC9p7bSMIqFRtvKvbhbRZeBBehLTTMv3OQsEZ8UHFLINCFQAjgWB9pTFUMAAABsklEQVQeAU/KeWXlE3y4Cl38g5id+1jUbWFIlo0Ls3hT+FIJs1AqNt5UfJwmYsFycrSIkH8c18BFHRPQFoZkbhPSV2L5iGQcJaziGGNWCIQAzmo6shgMmayO0kIPxIZSsQkN6bGVf/nMnhGSiIMsW5grfSKOtmQOWbzwgEGUig3aKwcf5hGXBPwCWPFktqrHctfh2F+tMufU4n0twcu9ReS1AzCMSwOBQEARCAEcS6EJAXzKhJaQchDt6NTK9HxZIlSWihKT9YkVuYc1RlIOBECfBp3YxaqXlYrNN1U+ffgBaMQU/zi9hUhXB9dSUaIxI7hhQuMOwWVysQplS6W66sRE54FAaQiEAC5txsoYL8n6yXFtKSf3qcKYnrnleaBTZ6ZEbCD63V1EjlCNmXcgsQupKOvJWFJxiOsCgZ1HIATwzi+BACAQCAQCgUBgDQRCAK+BevQZCAQCgUAgsPMIhADe+SUQAAQCgUAgEAisgUAI4DVQjz4DgUAgEAgEdh6BEMA7vwQCgEAgEAgEAoE1EAgBvAbq0WcgEAgEAoHAziMQAnjnl0AAEAgEAoFAILAGAv8HNbkw4JA6fzIAAAAASUVORK5CYII=\" width=\"240\" height=\"44\" alt=\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 240px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the stream, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transverse mixing coefficient, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" alt=\"u' = u - bar(u)\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"44\" alt=\"ubar = (1/h) integral(u(y),0\u003c=y\u003c=h)\" style=\"width: 103px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a (normalized) velocity profile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"30\" height=\"18\" alt=\"u(y)\" style=\"width: 30px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e specified at several points and computes the quantity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"215\" height=\"44\" alt=\"I = -integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 215px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = computeK(y,u)\r\n I = -integral(u'*integral(integral(u',0,y1),0,y),0,h);\r\nend","test_suite":"%%\r\nny = 1000;\r\ny = linspace(0,1,ny);\r\nu = y.*(1-y);\r\nI = computeK(y,u);\r\nI_correct = 1/7560;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = 2*y;\r\nu(y\u003e1/2) = 2*(1-y(y\u003e1/2));\r\nI = computeK(y,u);\r\nI_correct = 1/480;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 2.5;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.00788915;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 3;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01168232;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 3.2; \r\nb = 3.2;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01192484;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-16T01:19:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-16T01:18:30.000Z","updated_at":"2024-10-27T15:58:26.000Z","published_at":"2024-10-16T01:19:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = -\\\\frac{1}{hD}\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the stream, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transverse mixing coefficient, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u' = u - bar(u)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu^\\\\prime = u-{\\\\bar u}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ubar = (1/h) integral(u(y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\bar u} = \\\\frac{1}{h} \\\\int_0^h u(y) dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a (normalized) velocity profile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u(y)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e specified at several points and computes the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = -integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = -\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":43484,"title":"Integrate Me","description":"Given polynomial, output the integral (with k = 1 for simplicity purposes)\r\n\r\nExample:\r\n\r\ninput = [2 1] % 2x+1\r\noutput = [1 1 1] %x^2 + x + k","description_html":"\u003cp\u003eGiven polynomial, output the integral (with k = 1 for simplicity purposes)\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cp\u003einput = [2 1] % 2x+1\r\noutput = [1 1 1] %x^2 + x + k\u003c/p\u003e","function_template":"function y = integrateMe(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = [2 1];\r\ny_correct = [1 1 1] ;\r\nassert(isequal(integrateMe(x),y_correct))\r\n%%\r\nx = [2 1 9];\r\ny_correct = [2/3 1/2 9 1] ;\r\nassert(isequal(integrateMe(x),y_correct))\r\n%%\r\nx = [3 1 0];\r\ny_correct = [1 1/2 0 1] ;\r\nassert(isequal(integrateMe(x),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":13865,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-29T15:58:23.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-12T08:15:19.000Z","updated_at":"2026-02-20T13:48:11.000Z","published_at":"2016-10-12T08:15:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven polynomial, output the integral (with k = 1 for simplicity purposes)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003einput = [2 1] % 2x+1 output = [1 1 1] %x^2 + x + k\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50489,"title":"Find the area between curves (P1)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; 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10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 24.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.25px; text-align: left; transform-origin: 384px 12.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [3.5773, 6.1773, 5.5773, 11.2970]\r\n assert(isempty(strfind(filetext, num2str(ii))), ... \r\n 'Do NOT use provided answers in your solution')\r\nend\r\n%%\r\na = 1; \r\nb = 1;\r\n\r\ny_correct = 3.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 3; \r\nb = 0.3; \r\n\r\ny_correct = 6.1773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = -1;\r\nb = 4;\r\n\r\ny_correct = 5.5773;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = exp(1);\r\n\r\ny_correct = 11.2970;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":25,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T12:36:27.000Z","updated_at":"2026-01-23T10:01:56.000Z","published_at":"2021-02-19T12:40:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area between the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^2\\\\, \\\\mathrm{e}^{- x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51456,"title":"Compute an improper integral of a ratio of algebraic functions","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 105.083px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.5417px; transform-origin: 407px 52.5417px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 7.91667px; transform-origin: 152.742px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45.0833px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5417px; text-align: left; transform-origin: 384px 22.5417px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYIAAABaCAYAAAC14FF/AAAM9klEQVR4nO2dzZH6OhbFz3L2ZEDVrEmACKgJoDPoDMigUyCGDoEcejtLYiCFNwtzRgcjGX9IxrbOr8r16rX5gy3L90v3XgHGGGOMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjjDHGGGOMycYJwBnAN4Bd5PwewDFxzhhjzIrZA/h7HDcA/zz+e3yc3wH4ffydx2X+yzTGGFOKKxpBTy4IymD/+P/7479nBGVhZWCMMRvggEao71t/vz7+/odGCRzl3A5BGThMZIwxK+cbcYG+Q6MA/nl8JvXvTkWvzhhjTHHOaAT6oePcX+TcEVYExhizCk4IawAxof2FeLx/h0YBcHH4HPneOxwaMsaYRfOFIKwZ128LdA0B/aCx9L8en70hrCG0Q0TXx+eNMcYsFApwCn6mf94jn6VXoMcNwdqnQmGY6IbnLCNjjDELhFk/+9b//5P4/B6NxX9GPISk54+R88a0OaKZL54zxnyAPV4XeQ9IC3ljcsL1pRue15l+4TUlY2bjB/EFXmPm4Irn9aQDQmjRc9KYmWCxVywl1JiSsF1JG9adxM4ZYzKjWT7GzM0ecQOEdSc5FEGswNEYIzAsdP30hRgjUBGMSTn+QTOf6ek6Y82YN3BxzrFYsyS6Ktj7cEK8nsUY02KH8LI4O8gsiRumFSDSo/DalzFvUKvJaXpmKXyjUQRT0L5XntvGdKD7CBizBA7II7wZ8vQeGMa8wYtpZkmwsGxqVbGGPL+mXpQxW4bVxF4oNktghybTJ6YEhgpz7YXV3kDJGCPoy+K+LiYnJzQLvanwzBmhcniP4AmkNjTqMlSOaDxa7qF9QQh5tmsQ2DaFfbTaIdETgpdsT8JUAV8WW00mJ3s0QvSI58aFnGMXNMKWiuALodNt6ojNT3oQTA/lmoJ+Vzvr6PtxXT94DR2xY6731zZVQWst1mbamBxoVtoJjbC9Iux3cUSw0lNHzDI/IG25M1uoy9PVNYQf+T4qnCOcaWQqQF8EVxSbUrTn2R+me5/cMClVdUxF8G43PBpC7Hjq8KipDrXUvGuYKYm2lc5RtMhwUCrFlOffZcJpeMjvQMUwVshYJY87gru4VWIxUmNKoHNtarilHWqK0betRJ/vMhWhE6KWSaGLeHaJTUk0O22qcaXhnJhSGfJbmj7tXkTmSRGkJtjWUMVnTCl2ePa4p9SraLv0VEbPu7BR7LNeJzMAnl3XGipstRmXW0uYklzxXE8wReCqtR8LZ6pB9y71k7UEmkJtKocZCLW4iNz5yZaQKckZYc9hNbYIU0eHfF8qfNv2PKgovvGapXRESBVV5cEQKf9uKkLjhLUUVmnBjVtLmFzsEYTpF55TRdsC94DhqaTqEei85VaXOq9Z1PYL4N8IdQGsF+B17lrfmavXkVkZOrlqaVerHpAtH5MLWuT3x6HCVAUuq3eHCtu21f+DkPXHNhQa4qWiUQXBzyqa3nqLnDcVoDHCGkrK9YXMkcVhDNH+PTEhf35zvg9HPAvuX/muI4KSoXWvvxtTAkBjDN07zpsKyGUdawbC2GOOVg+6UOwFMmNM9Wg62tRil7UoAnWfvVBsjKmeGrNnNF5aQyjMGGM6qTF7prZUWWOM6UQzEGpIF2svFNdwz8YYk0TXB2ppK+GFYmOMEdo5x1NZw2Kx3nN7Cz9jjKkOFdw5YuVrUARLXyj+D4D/+vDhw8fE41/oiQrgGtpKAMtfKLYi8OHDR46jlyKose004IViY4z5PxoiqSVW7oViY4xB6IjYjs3/YvvbNWrxXC3KD2gU4BLDYJ/iiCZp4Ixte4U7NJ4/73UJ4d8DQnO8rcubOe61pvHMRo0bdbNbZU2KLwXbK9/w2rRta6HRA8Jz13WxTxaNXh7XpEklf9hm08c57rWm8cyKDlgt2pOdZa0ImuevnhGF5acFZG52eO1uqq3mP+EFcYMeQqW8xdY2c9xrTeOZHQ2F1aA1tV3xWhXBAXmsdW7c0obhwrWOT4wvxD1ergvquT3m8YZiG/BoQeuWPLI57rWm8cyK7sI2R4fTT0OrkJNjjYLuC/lqPfaIK38mEKxpfLjT2NDzLKZURXBAY0GWNoxS7e23KLim3mtqrub8jWrRjKEaXKczwgu/NkEH5FUCXXBeLHnN6BvNnNVY/5gXnYqgLUT2CEbD3Kxxbo4lda/cQU5D12PnY03jOQptLbGleHAM7klL1jY5TpivtoXzYumhQm2WOPZZXpH2hjln5rQkqYRryGjrc6+azDJmg7CaxnM0uh3nllMGgUZQ6ERakyLY43Wv35LcsGxvQJliLTI02iVgfpCn51hfLljPvJxKn3tVY3WMQq5pPEejbteWOeM1pJJbEfygGc8p25qmuGC+0N03nj2nqTDeXkKYaieAMUryF+9DbUw1LvFc2zBjK6cnVnJeTqHvvU7J+ikxnpukhkIyxnrb1kTu+6ZSze2C0mqdwxs4oBmTnKEQuuYlkhEYNrhj+DV/ob9yuiCvcoyxQzOHcj/nUvNyCn3vVUN/Q0PXpcZzc2ha1VrCAGM4o3mJr62DAuSKPAuwpV64OYQQEHKuc784JRUBF4qHWotDY/98V0oKlV+UEdZLVAR973VKnUep8dwc6lYvzW3MibZO0IPCKVcZeqkX7o7ymUJd1tPUsSmlCDT1eciYp7wetp5IUfI5XBC/hxOme2dLUwRD7pVrmEMX7EuO5+boswizR+jZsSQX64DmmjjJ2xYzM2y6qqXXEBqiEB0jjI9orKI/hBj9CeE6+TzpCcSum89+CqUUgVqLLLCj98e/X/A8t+kJtOfy7vHZrjnOVNUuxszLC+IhqmPi70MprQj2CAuy9LZPaK6dhhYZeq8cq9/W5/h8b3hV3qXHc3NwgqSE4RkhU4UVqEsZyG8016WpZXyxvtBcNydRyopbgyKgsh6ihHcIL8s3giDUUKDG1PXFih1Tm7KVUgS8blaTUhCpINZnzGLC1H2+E/J8Fl0W5dB5qQ0fY8eSPVUgjMkFYZ60x5lzd+i9HlrnOH4/j0P3lacymGM8NwcfVmx9gGEjnTz7js9/Cl1M+kGw+Dgpu6pNc3cmLPHC0TXu685qb5XYdXCsqNBpwaaOHONTShFQENDrad+vKoMDnjuOxo53ynaIUu4zL//95npy1fWUXLuKeV36mwzp0Fsbcq8q1M94bR+hxbBskDjHeG4KnaixuCiVRNsa/EPzAi6hdS+h4GP3zE+FsEq8cPzOPqgSSCnrMTH1qZRQBCoEboi/5Br6zLEGRuOo73dteV5SCVwRN1L4m1MiCJrQEeshBLx6fWYgulDcfpB0yWIvLifAUhaegPnaaKtgmXIMyWkeoggYKkktrKnwzK3Ic4zLEKGhzzwljPR55RDCHL++luVW56Va6ql/MzUUo4Zql/LVOWBGwMkT06RfHec0JrgU5sp+WrIiUCGfUtIUTLnrBIA84zJEEei+CanxVIsyx/0OVQRbnJcsrut6XnrfYw0O/Y7U7+icd9hnJHxJulzqLkWwJFdsbBphbj4ZGmrHZNvoCzy3Es8dGtLnnRISalHmut+hGVxbnJeqdN4p4CkGh7a+Sf2OelxLClWviq5BXpsi0EXBT7qIJRQBwz1dqMBJCT19gefOnMitCDRtNGVpa51IrvYCQzO4tjgvuXaYEvJqpU9RwFoouDTDZjPwYaXS5dakCJgqqBbEpyiZPtolzFQwxoQ8G9bxM3MX1ORWBO+KjPR+SzyLPtbnFudlH4NDQ3Zjw2F9PCkNc9obGAkndGoBi/G5LkWwhHqCI0JKXqz5GP8+FyUUQZ9Mla7sGGYStd31Q+SzpcitCN7FqCmMYmmNU2CB1Du2Oi/V2o/JDjZG1HDNbsTvvluM5pjO2Y13k/BFSVmZ1Mgxj+GTWUM7hLqAdoVouzlVqb45XZRQBLyvrsUw9Qj0t7ViWIUjx26ujow5FcG7/lhdue1TuSGufGqZl11rMxc51FL/w/BQpBY4xjIa77ASGMQRry87H+a7mGVXHcG7UEUpdILc8Tqx1S29Rc6XplThDgumUmi8lAKSlZe8Fh2XWIuFkuRUBGottreWZI1LiTUQKqDYd9c0L9Xi/0Vo6UHF267oHvObqTCmRiMcDupJyr2ixn4nCLoqiz+1OKMLgKmGUveO86UppQho8XdN/iOCwGFzNH3uFFa/mN+SKrFYzPu5IoS+vlFOQLDdSupcLfOS20eqMtAwF+XOGE9Af+MHwWjhM75g3pDaJogV01CQ943v06qk28sXzt374nADkBIW6Q3Lau0xBG5Ms+ain1T18hooOS/NwmHmBCcvBfnQ3N49Qp8O7/LzOY5YXmuPWsi9Y5sxs3JAY/3/InRlNOtl7r1zTTCobAQZYxaDd12alymxbmOMKQI3ULFwKo/H2RizaJiTbspwgvPUjTHGGGOMMcYYY4wxxhhjjDHGmO3xP3imVLpU2b9fAAAAAElFTkSuQmCC\" alt=\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\" style=\"width: 193px; height: 45px;\" width=\"193\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ea\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eb\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 138.217px 7.91667px; transform-origin: 138.217px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are positive real numbers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = integRatioAlg(a,b)\r\n y = f(a,b);\r\nend","test_suite":"%%\r\na = 2;\r\nb = 1; \r\ny_correct = 0.523598775598299;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 3; \r\nb = 1; \r\ny_correct = 0.392699081698724;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 5; \r\nb = 2; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 4;\r\nb = 5; \r\ny_correct = 0.174532925199433;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 7; \r\nb = 6; \r\ny_correct = 0.120830486676530;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 1; \r\nb = 6; \r\ny_correct = 0.224399475256414;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 9; \r\ny_correct = 0.092399783929112;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 8; \r\nb = 3; \r\ny_correct = 0.142799666072263;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 11; \r\nb = 13; \r\ny_correct = 0.065449846949787;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 19; \r\nb = 17; \r\ny_correct = 0.043633231299858;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 23; \r\nb = 29; \r\ny_correct = 0.030207621669133;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 31; \r\nb = 37; \r\ny_correct = 0.023099945982278;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 41; \r\nb = 43; \r\ny_correct = 0.018699956271368;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 59; \r\nb = 53; \r\ny_correct = 0.014024967203526;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 61; \r\nb = 67; \r\ny_correct = 0.012271846303085;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 79; \r\nb = 71; \r\ny_correct = 0.010471975511966;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 83; \r\nb = 89; \r\ny_correct = 0.009132536783691;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 91; \r\nb = 97; \r\ny_correct = 0.008355299610611;\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\na = 50*rand;\r\nb = 0;\r\ny_correct = pi/(2*a);\r\nassert(abs(integRatioAlg(a,b)-y_correct)\u003c1e-13)\r\n\r\n%%\r\nfiletext = fileread('integRatioAlg.m');\r\nillegalfns = contains(filetext, 'integral') || contains(filetext, 'quad'); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-04-17T03:39:24.000Z","updated_at":"2021-04-17T03:42:40.000Z","published_at":"2021-04-17T03:42:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"integral(x^2 dx/(x^4 + (a^2+b^2)x^2 + a^2b^2),{x,0,infinity})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\infty\\\\frac{x^2dx}{x^4+(a^2+b^2)x^2+a^2b^2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are positive real numbers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50504,"title":"Find the area between curves (P3)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 541px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 270.5px; transform-origin: 407px 270.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"87.5\" height=\"18\" style=\"width: 87.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.4208, 0.5101, 0.2569, 0.1252, 1.1838]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1; \r\nb = 0.5;\r\n\r\ny_correct = 0.4208;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nb = 0.5; \r\n\r\ny_correct = 0.5101;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(1); \r\nb = 1; \r\n\r\ny_correct = 0.2569;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0.5;\r\nb = 0.4;\r\n\r\ny_correct = 0.1252;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = sqrt(2);\r\nb = 0.1;\r\n\r\ny_correct = 1.1838;\r\nassert(abs(AreaCurves(a,b)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T18:50:42.000Z","updated_at":"2026-02-05T14:11:12.000Z","published_at":"2021-02-19T18:51:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = sin(ax)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = bx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for different \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eb\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml 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w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=1 , 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":685,"title":"Image Processing 2.1.1 Planck Integral","description":"Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\r\n\r\nPlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\r\n\r\nc1'=1.88365e23; % sec^-1 cm^-2 micron^3\r\n\r\nc2=1.43879e4; % micron K\r\n\r\nMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\r\n\r\nRadiance : L = Me/pi in units of ph sec^-1 m^-2\r\n\r\nInput: (3.0 5.0 250) : From 3um to 5um at 250K\r\n\r\nOutput: 4.9612 E+018 : units ph/sec/m^2/ster\r\n\r\nPerformance Rqmts: \r\n\r\nAccuracy: \u003c0.001% error\r\n\r\nTime: \u003c100 msec (using cputime function)\r\n\r\n\r\nCorollary problem will include spectral transmission and emissivity.\r\n\r\n\r\nIR Calibration Reference:\r\n\r\n\u003chttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003e","description_html":"\u003cp\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/p\u003e\u003cp\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/p\u003e\u003cp\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/p\u003e\u003cp\u003ec2=1.43879e4; % micron K\u003c/p\u003e\u003cp\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/p\u003e\u003cp\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/p\u003e\u003cp\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/p\u003e\u003cp\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/p\u003e\u003cp\u003ePerformance Rqmts:\u003c/p\u003e\u003cp\u003eAccuracy: \u0026lt;0.001% error\u003c/p\u003e\u003cp\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/p\u003e\u003cp\u003eCorollary problem will include spectral transmission and emissivity.\u003c/p\u003e\u003cp\u003eIR Calibration Reference:\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\"\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function Radiance = Calc_Radiance(Lo,Hi,T)\r\n% Lo wavelength um\r\n% Hi wavelength um\r\n% T Blackbody Temperature (K)\r\n\r\n Radiance = T;\r\nend","test_suite":"%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=250.0;\r\n% Radiance = 4.96124998 e18 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.96124998e18; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=300.0;\r\n% Radiance = 4.1826971 e19 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.1826971e19; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=8.0;\r\nhi=12.0;\r\nT=280.0;\r\n% Radiance = 1.37122128 e21 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 1.37122128e21; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\n\r\n% Add random to block answer writers\r\nlo=3.0+rand\r\nhi=5.0+rand\r\nT=250.0;\r\n% Radiance = To be calculated ph/m2/sec/ster\r\n\r\nc1p=1.88365e23; % sec^-1cm^-2micron^3\r\nc2=1.43879e4; % micron K\r\nsteps=1000;\r\n\r\nx=lo:(hi-lo)/steps:hi;\r\n\r\n% Planck Vectorized for Trapz\r\ny=1e8./(x.^4.*(exp(c2./(x.*T))-1));\r\n% Leading 1e8 is for numerical processing accuracy\r\n\r\nz=trapz(x,y);\r\nrad_correct=z*1e4*c1p/pi()/1e8 % 1e4 normalizes from cm-2 to m-2\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-14T04:31:21.000Z","updated_at":"2025-12-10T03:26:46.000Z","published_at":"2012-05-14T05:39:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec2=1.43879e4; % micron K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePerformance Rqmts:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAccuracy: \u0026lt;0.001% error\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCorollary problem will include spectral transmission and emissivity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIR Calibration Reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":59676,"title":"Write a code to implement the improved Euler's method to integrate a simple function","description":"Euler's method approximates the solution to a differential equation as\r\n\r\nwhere . It's possible to improve on Euler's method by doing the following:\r\n\r\n\r\nThe challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's improved method to integrate over equally-spaced points ( equal intervals) between times and . You must implement the boundary condition . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 227.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 113.75px; transform-origin: 407.5px 113.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eEuler's method approximates the solution to a differential equation as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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\" width=\"177\" height=\"18.5\" style=\"width: 177px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44.5\" height=\"18\" style=\"width: 44.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. It's possible to improve on Euler's method by doing the following:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"283.5\" height=\"34.5\" style=\"width: 283.5px; height: 34.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63.8333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 31.9167px; text-align: left; transform-origin: 384.5px 31.9167px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's improved method to integrate over \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eN\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equally-spaced points (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39.5\" height=\"18\" style=\"width: 39.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e equal intervals) between times \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"14\" height=\"20\" style=\"width: 14px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. You must implement the boundary condition \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"63\" height=\"18.5\" style=\"width: 63px; height: 18.5px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [t,x] = EulerImprovedIntegration(t0,tf,N,x0,func)\r\n t = 0;\r\n x = 0;\r\nend","test_suite":"%%\r\nt0=0; tf=1.5; \r\nfunc = @(t,x) 2*x*t;\r\nf=func;\r\nN=50;\r\nt = linspace(t0,tf,N);\r\nh = (tf-t0)/(N-1);\r\nnum_steps = length(t) - 1;\r\nx = zeros(1,num_steps + 1);\r\nx(1) = 1;\r\nfor i = 1:num_steps\r\n xstar = x(i) + h*f(t(i),x(i));\r\n x(i+1) = x(i) + h/2*(f(t(i),x(i)) + f(t(i+1),xstar));\r\nend\r\n\r\nx0=1;\r\n[t2,x2] = EulerImprovedIntegration(t0,tf,N,x0,func)\r\n\r\nassert(isequal(x(1),x2(1)))\r\nn1 = length(x);\r\nn2 = length(x2);\r\nassert(isequal(x(n1),x2(n2)))\r\nassert(isequal(n1,n2))\r\n\r\n%%\r\nt0=0; tf=1.5; \r\nfunc = @(t,x) x+t;\r\nf=func;\r\nN=50;\r\nt = linspace(t0,tf,N);\r\nh = (tf-t0)/(N-1);\r\nnum_steps = length(t) - 1;\r\nx = zeros(1,num_steps + 1);\r\nx(1) = 1;\r\nfor i = 1:num_steps\r\n xstar = x(i) + h*f(t(i),x(i));\r\n x(i+1) = x(i) + h/2*(f(t(i),x(i)) + f(t(i+1),xstar));\r\nend\r\n\r\nx0=1;\r\n[t2,x2] = EulerImprovedIntegration(t0,tf,N,x0,func)\r\n\r\nassert(isequal(x(1),x2(1)))\r\nn1 = length(x);\r\nn2 = length(x2);\r\nassert(isequal(x(n1),x2(n2)))\r\nassert(isequal(n1,n2))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4078801,"edited_by":4078801,"edited_at":"2024-03-05T14:42:54.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12,"test_suite_updated_at":"2024-03-05T14:42:54.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-02-29T19:23:54.000Z","updated_at":"2026-03-31T11:25:40.000Z","published_at":"2024-02-29T19:23:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEuler's method approximates the solution to a differential equation as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t+\\\\Delta t) = x(t) + h \\\\cdot f(x, t )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh = \\\\Delta t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. It's possible to improve on Euler's method by doing the following:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex^* = x(t) + h \\\\cdot f(x,t)\\n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(t+\\\\Delta t) = x(t) + \\\\frac{h}{2} \\\\cdot (f(x,t) + f(t+\\\\Delta t, x^* ) )\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe challenge is to write a code that can take some arbitrary function, f(t,x), and use Euler's improved method to integrate over \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equally-spaced points (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eN-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e equal intervals) between times \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_o\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et_f\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. You must implement the boundary condition \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex(0)=x0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43290,"title":"Calculate numerical integration.","description":" x=0:0.01:1\r\n y=@(x)x.^2\r\n\r\nUsing given two inputs(x and y), conduct numerical integration in x.\r\n\r\n(hint: trapz)","description_html":"\u003cpre class=\"language-matlab\"\u003ex=0:0.01:1\r\ny=@(x)x.^2\r\n\u003c/pre\u003e\u003cp\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/p\u003e\u003cp\u003e(hint: trapz)\u003c/p\u003e","function_template":"function z = integralx2(x,y)\r\n z=\r\nend","test_suite":"%%\r\nx=0:0.01:1;\r\ny=@(x)x.^2\r\nz_correct = 0.3334\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n\r\n\r\n%%\r\nx=0:0.01:1;\r\ny=@(x)x.^3\r\nz_correct = 0.25\r\nassert(abs(integralx2(x,y)-z_correct)\u003c0.001)\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":0,"created_by":33533,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2016-10-15T05:49:20.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-10-10T05:41:31.000Z","updated_at":"2025-11-29T14:58:18.000Z","published_at":"2016-10-10T05:41:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x=0:0.01:1\\ny=@(x)x.^2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing given two inputs(x and y), conduct numerical integration in x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e(hint: trapz)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":50499,"title":"Find the area between curves (P2)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 612.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 306.25px; transform-origin: 407px 306.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Area between curves - Problem 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 32.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 16.25px; text-align: left; transform-origin: 384px 16.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Find the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAAAoCAYAAADXNiVcAAAG+0lEQVR4Xu2aBYilVRiGn7XFLmxFVOxO7E5UFLu7u8Uu7MIWxU4UO1CxsAsTE+zC7g6e5Ttyd/afmXPuf2dn9t57YNlh5vwnvvfL9zvD6I6OlcCwjr159+J0we9gJeiC3wW/gyXQwVfvWn4X/A6WQAdffbAt3/2XAD4BPmoBDjMC0wPPAP+2YL22XmIwwR8L2AX4BrihRWCNAWwOjA1cDfzV1ujVvFwrwHeNWYHlgSmB14BHgJ/7OJvA7wN82kLg03aeZ1NgvK4C9K0ddcEfHzgAWBrYD5gFuAc4Azgc+L2X7QVnGeCQfpSkWd32XCcCdwEPNbtIu39XB/wxgf0DdMF8LH4+E7gZ2BH4vkKAswNnAQcBbwyggOcATgH2Bd4fwH2GytILAKsAi8Nw8m5vYF7gKGAeYFvgzsbD1gF/0QD5YWDPsODJgXWBp4C3KqSiwhwN/AqcCvw9gJLzbnqjSYFjB3ivAbxG0dLLAY+G1zWBHgf4GLgPOL6nHJoFP4F4JLAlcG3mEdXAS4DdgFcyv6kzbX7gQmBn4PU6C40m324BnAZcB7wDXAasBdwObADc2grLN7ZfD2jpGxYAqSUuBOwB/DgKBDoRcD7wUoSadi7/tPKTw9tdEbnYt+EFxGiTnt64WctXi24Jd7IV8FUGkJMAlwIvAidlzG/VlMOAhfvIQVq1z2CvM1144KmBHSL0Jpn/AuwF/FDX8hs17ILQsN8ybq4LNhE8ELgjY36rppiDnABsDLzZqkWH4DpWXPcCFwNHRKU1J3BTuP/zeuY9uZZv6WSGLinT2+hPEVYFrgTWAV7IEN4EwGLA+sDqwFQ9MlZduhWDIeSB0OwvK9ZdJLLcbWJextZDYspkwFLARsAKgAZmTE+ymwY4LjgNY/tnAbou/v64gR5a0K3GfgI+AL5Ot8sFv1EaS8biCn+1AoFuHaXhSLGnF1HPEL//M5IYw4usnWD/E6FDpZQeliV0/Q8r1rLkuxGwBL2qEFaFfU3hN1XT5TSeKFzHkvg7QNdtkrxi3NkkWzJNLsWqSaN6LnKo2UIOlrbJQ1uVnQ3MFF7Bb4aPZsBXyFqwGqhGvZt5KQ+9UmivzF7J0ONcFHuqBHoPSxiTzv6SOAUifWzGa7lTMgYT/HROKyvPbe5yN7B7cBfex7LOMXNk+CqBxJnkWuJhlLteW+UfgXcpBb/xIH0ROVUC9hDGJQX6v+vJRCK57mlDe00wj8nk7qeIREjLKwU/83gDPs28RbBfBV4OQs3kuT/F7/NgpeCn7NG4InHiv9wD1AE/ZbLGPkklrd9OYM5oB/BTsmwoMHSNlLnnCKLnnFLwkwvVEnX5xtLcUcft26QxxunydGGHAn9kbpxivmcdlSVm5vGyppn8me+sHXmTMqg9SsFP9KHsUQm540FLE77Gy3lOM3u5eqnKXG7BNRL4Ml+5TGRtwbZ4gXGB04NGt5STLPs/cWt2r1LwU+L1YPTNq0qr3s5SWuo1rpP6CCY2pYpnnvF4tJxtPpWMoZDwed71wvKtsGyXe67SpHmke5eA3yy5kzZNFmiXqYTkkbE6J0rK7aP2LeknWFrqNUoqk3TmoQD+XBGu5OUNWxMCazZROtYCvzHu7BpZd4kVJZ797ei15ySKPvo4OFqyZrvGfb2PQjCHsN5fNjjrLyoOk6oTq4TUeSw582DPleiSr7eysjFl3F8DSPJXPtb/PlsbgbrNOXiJ5SeqcL4mXajnkXM2afF/mw49h+eZOGhIXwJtBkgqWbsa41LYSXHfLqFEk0xX1cMRyRAFpvBkwYb68BmaFZVsnuSWD2VUcGt0R6r3jfv+zXBgNSOLl2NMI9y/BHxjtrThkxHvpQpLh93Ay8Oan634eEHgtugW6iFk7Gz/Jqv2oYJ/15L1BFKWCqHK6l1+5fAQPmQYHR50aBgSVwL/Xli0ni89iUsNNTuiGsDnQf709WSuV4xKwDfDVAPrZJvphYmvbKueeRnfde2SGrJy5gdeMA3pXB+DWDl4eX/u7dWvGbIPRnxTWJsQKdXyJuebF9mCtu3t/1Yoja1v+xv+Tm+nESkrqe2mRi74jY2dkmSr6lApgbN0eb6pU+d9ZFkqLyAhUlKV5K3eBrNywU8Mm0pgHNYl1RmWXzZofME7EMCMKgWrI4NB/zYX/NQrtjvUivdw7mvWOnckK7298m1GQCqojzbNgKWCixOhZjYdHb+pAl8ixWdAPq7cLvrEAm7yJLMmydKK4d726eWtz20FYwUIvG7eZNKOVxf4PpCqAj910My0dfH2gSVZdNGphdgK8NMaPkqwjKt65l26j6WdiV5u06d0/baaXwW+xIF1+E7A04BEg+D7CLI72kgCuTG/ja7cvUqSQBf8DtaFLvhd8DtYAh189f8AQYWAOJHhcZoAAAAASUVORK5CYII=\" width=\"63.5\" height=\"20\" style=\"width: 63.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"68\" height=\"32\" style=\"width: 68px; height: 32px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; 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\" 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src=\"data:image/png;base64,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\" width=\"32.5\" height=\"19\" style=\"width: 32.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"29.5\" height=\"19\" style=\"width: 29.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"76.5\" height=\"18\" style=\"width: 76.5px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [0.5, 0.6667, 1.3606, 2.7754, 22.3242]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\n\r\n%%\r\na = 1; \r\nn = 3;\r\n\r\ny_correct = 0.5;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1; \r\nn = 5; \r\n\r\ny_correct = 0.6667;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2; \r\nn = 2.5; \r\n\r\ny_correct = 1.3606;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nn = 3.1;\r\n\r\ny_correct = 2.7754;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = exp(3);\r\nn = 12;\r\n\r\ny_correct = 22.3242;\r\nassert(abs(AreaCurves(a,n)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-19T15:56:21.000Z","updated_at":"2025-08-25T11:22:08.000Z","published_at":"2021-02-19T15:59:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Area between curves - Problem 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Find the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x) = x^{n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x) = ax^{\\\\frac{1}{n}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e for different \\\"n\\\" and \\\"a\\\" coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e Plot of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eg(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea = 1, 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ePGdevW7c9//nN4eLgQYvjw4Xq9/vvvv7ddHpWWlppMpmHDhjm8keXLl//hD38YMmSIECI8PHzEiBHbtm0bOXLk8OHDjx49um/fvpCQkI4d7ZfdoaGhnTt3vnLlSptDHjx4sHv7HTlyxPXNejC22WyOiIj4n//5HyFE7969Kyoq2hw+2FSlxRj+8q31T7uuy8kIcEitW3Y5OTlRUVHr169ft26d0rOow6JFi7777rtPPvnE9jdv586dhRApKSnWj9TX1wshIiIiWt/CuXPn+vTpEx8fb/3It99+K4RYsmSJEGL8+PHLly+fPn167969W183IiLi1q1bbQ45e/bsPn36uP09/a/ExEQXn/Vs7I4dO37xxRdCiLt37164cGHDhg3tnUqTfrgR144IUR24Q61n2ZnNZp1OV1BQ8OabbxYWFrY+wGAw2F4M8jPuvvjii3/9138dOHCg3SsOPPnkk+fPn29oaLA+hn/w4MF58+Z99tlnrR81qaqq0ul0er3ecvHhw4fh4eGxsbGtT0hr7Zlnnrl69erXX3/ti++mfbwZu7Cw8C9/+cvo0aN/9rOf+XlMeXn2aJA6f69AYWpdIbnzFJkgj5CtHTt2CCHszim4ffv2+fPnhw4dantGmeUZrK233YQQtosMIUReXp7JZEpOTnZnAJ1Od//+fQ8m9543Y48dO3bs2LHTp0+vq6sLnveN5XwEKEWtjyGhXSy7T3a/hfPy8oQQSUlJth/s1KmTEKK5ubnN27QsTKdMmeLOAPX19QMGDHB7Xj9yc+z6+vq9e/da/j516tT33nvP75MpyrOnplbOiamcE8NDQfAVta6Q4L7m5mbLeW4TJ060/bjlpQdsH0ASQnTp0kUI0dTU1ObNnjhxQvywZ2az2Ww2O1xdXbt2zbpp5sKpU6e2bt3a5mF2fvnLX7p+GMmWm2Pn5eX9+te/XrhwoRCirq7u8ccfb+9U8vNsJXT69Jlu/2+G9SJvxAcfIkja17Fjx5CQkNDQUEtsrIqKioQQEyZMsP2g5Yw7y6kNdu7evVtaWmp5itLDhw9PnToVExMTGxtrPWDHjh09evSYP3++w+s+8sgjbY762GOPTZ061a3v6ofXcvFZz8ZOTU2trq4uKSnp1q1bXl7e9u3b2zuVhDwukO1F2xoBvkWQtE+n0yUmJpaUlFjOBLF8cM+ePeXl5XYPIAkhevXqFRERUVZWZncjZrN51KhRFRUVBw4cmDt37qeffmoymUaOHGk9oLm5ee/evcePH289QF1dnclkcmcRExsbu3jx4nZ/h855PHb37t3feeedr7766vr166dOnfLJy/opwicRcoblEXxL3UEaN26cw1PsYGf9+vXJycmHDx+2vA3Ehx9+aDld3u4BJIspU6ZcunTJ7oNGo7GioqJbt25Dhw5tbm7eunVrcnLy9evXrQe89NJL6enpoaGhrW+wpKRE/N/aK8C8GVsIYZsuFfEgQm4WiM06+JW6gwQ3jR07Njc3d+3atR999NHDhw9nzpw5efLknTt32j2AZDF58uQVK1Y0Nzfb/pru0aPH3LlzO3XqVFJS8qtf/Wr9+vVxcXE//elPV6xYMWTIkCNHjixdunT69OkOv/qJEyeio6MV+eXuzdjq4r8IWbFZB39T6/OQ2sSrfbs2ePDgioqKW7dutX7BU6PR2Lt3771797Z+ebeqqqrq6urx48dbH44qKiq6c+dOSkqKw3MZLBISEmbOnLlx40bffgvu82xs+QUgQrZYHsHfCFIwunnzZs+ePYcOHXru3DmHB7z00ku1tbWWk8W9VFJS8vTTT1+6dMmds+zQpgBHyMpueUSQ4A8q/s9DuOPGjRuvvvpqv379bBcoe/bsEUI4PB3OIj09PT4+/tKlS96/CcWmTZteeOEFauSN9kbIJwVygRrBT1ghadzq1at/97vf9enTx3om94ULF5KSkp544onjx487ezBfCJGZmVlWVnb48GFvvvrZs2cnTpxYUVHh8AXu4IJUEWJ5hMBQ68mscFNcXJwQYvHixWfOnLlw4UJOTs6ECRMWLVqUm5vrokZCiMzMzJs3b3rz1uPNzc3PP//8n/70J2rkpva+XMLp02esf/w82j9RI/gPKyTtO3v27Pnz56urqy3vNDF+/PhevXq5c8UbN27MmjVr69atnp2xvXjx4tGjR69cudKD6wYPqVZCDrE8QsDwGJL2DR8+fPjw4R5csVevXkeOHMnOzvYgSKdOnZo8ebJvn+WqGfJHyBlqBL9ihQQEgkojxPIIgcQKCfAXlUbIGWoEfyNIgI+1q0MyR4iXZkCAESTABzQTIWdYHiEACBLgIY3tyNlheYTAI0hA+2h+MdQayyMEBkEC2hZsEWJ5BEUQJMCpYOuQBad6QykECfiB4IyQM9QIgUSQACHa0yFtR4jNOiiIICF4sRhyjeURAowgIeiwGHKG5RGURZAQLOhQu7A8QuARJGic++8t5OdBZMfyCIojSNAgFkNeYnkERRAkaAcd8hjLI8iAIEH12JTzEs+EhSQIEtSKDvkDNYKCCBJUhg75Fpt1kAdBgjrQoQBgeQRlyRuk2traysrK2NhYg8Hg8ICrV69WV1f369dv0KBBAZ4NAUOH/IrlEaQiaZCOHj26YcOGMWPGnDlzJjU1ddWqVXYH7N69e+fOnWPGjDl//vxPfvKTrKwsReaEn9ChAOBcBshGxiCZTKbMzMwDBw7o9fqGhoaJEyempqbGxcVZDzCbzZs3bz58+PDAgQNv376dmJi4cOFC1kkaQIeAYCZjkE6cOBEZGanX64UQUVFRycnJJ0+etA2SEKKlpSU8PFwI0blzZ51O19zc3Pp2bPf6Kisr/Ts0vECHAo/lESQkY5AaGxsTEhKsF7t27VpVVWV7gE6ny8zMXLFiRUpKSnFx8fz584cNG9b6doiQ5OiQJKgRJCFjkEwmk06ns17U6XRms9numNOnT3fp0qVXr16RkZFff/31vXv3unTpEtgx4Tl3UkSH/IdzGSAnGYMUFhZmMpmsF81mc2hoqO0B+fn5paWlubm5ISEhzz333Isvvrhr166VK1cGfFK0Dx2SEMsjyEPGIEVHR1+4cMF60Wg0Tp061fYAo9EYHx8fEhJiudi/f//a2tqAjoj2oENSYXkEaenaPiTgRo4cKYQoKCgQQly+fLm4uDgxMVEIUVZWVl9fL4QYPHhwUVHRlStXhBC3b98+ffr0qFGjFB0ZDnTo8L9/XDh9+ozlT6CGCnacywCZybhC0ul0mzdvXr16tV6vLy8vz87O7tmzpxAiJydn2rRpaWlpgwYNWrt27bx585544ony8vI5c+bMmTNH6anxT20uiSiQDKgRZNOhpaVF6Rn8wmAwcJZdgLE1JzmWR5CcjCskqA5LItWhRpAQQYLn6JCKcC4D5EeQ4AlSpC5s1kEVCBLagQ5pADWCtAgS3NLm2duBGgTtxmYd1IIgwRWWRGrHZh1UhCDBMZZEAAKMIMEeKdIMlkdQF4KE/0WHtI0aQX4ECaRImziXAapDkIIaKdIqNuugRgQpSLlIER3SGGoEtSBIwYUlUTBgsw4qRZCCBSkKEmzWQb0IkvaRoqBFjaAuBEnLSFGwYbMOqkaQtIlzFoIQm3VQO4KkNaQIghpBnQiSdpCiYMZmHTSAIGkBKQpybNZBGwiSupEi2KFGUC+CpFakCBZs1kEzCJIqOasRKQo2bNZBSwiSypAiOEONoHYESTVIEeywWQeNIUgqwMNFaI3NOmgPQZIdCyO0iRpBG+QNUm1tbWVlZWxsrMFgcHhAQ0PD2bNnIyIiRo8eHeDZAoMUwRk266BJkgbp6NGjGzZsGDNmzJkzZ1JTU1etWmV3QEFBQXp6+pgxY2pqasLCwj766COdTqfIqP5AiuACm3XQqg4tLS1Kz2DPZDKNHDnywIEDer2+oaFh4sSJhw8fjouLsz1g7NixOTk5o0aNEkJMnz595cqVU6ZMsb0Rg8FQWVkZ4Ml9wmGNSBEsqBE0TMYV0okTJyIjI/V6vRAiKioqOTn55MmTtkEqKCjo16+fpUZCiM8//9zh7dju9akiTiyMAAQzGYPU2NiYkJBgvdi1a9eqqirbA4xGY2xsbEZGxmeffRYSEvLKK68sXbq09e2oIkIWpAjuYHkEbZPxcReTyWT7gJBOpzObzbYHVFdX5+bmPvHEE2VlZfv379+xY8fJkycDPqbPONujo0awRY2geTIGKSwszGQyWS+azeaOHX+wknv88cf79+8/f/58IYTBYJg0adJf//rXQE/pCx068IgRPEGNoEkybtlFR0dfuHDBetFoNE6dOtX2gB49etheVOn5daQI7uM8bwQDGX+Vjxw5UghRUFAghLh8+XJxcXFiYqIQoqysrL6+XggxYcKEhoaG48ePCyEaGhoKCwtnzFDTjysLI7QLm3UIEjKe9i2EKCkpWb16tV6vLy8vz8rKspzS/eKLL06bNi0tLU0Icfr06TfeeKN3797V1dU///nPV6xYYXcL0p72TYrQLtQIwUPSIHlPwiBxKh08QJAQPGR8DEmTWBjBA9QIQUXGx5C0hxrBA9QIwYYVkn+RIniGGiEIsULyI2oEAO5jheQvrWtEiuAmlkcITgTJ91gYwRvUCEGLLTsfo0bwBjVCMGOF5Ets08EbvD4QghwrJJ+hRvAtlkcINgTJN6gRvMRmHUCQfIAawUvUCBA8huQlUgTvUSPAghWS56gRvMeJDIAVQfIQNYI/sDxCMCNInqBG8Ak26wBbBKndqBF8ghoBdghS+3ToIOze0ZAawQPUCGiNILWDZW1ku0KiRvCAbY1IEWBFkNzFTh18wm5tVJUWQ5MAC4LkFmoEP6FGgBVBahs1gq/w0BHgAkFqAzWCr1AjwDWC1D7UCJ6hRkCbCJIrdssjagTPUCPAHQTJKWoEn+DV6gA3ESTHqBF8onWNWB4BzhAkB6gRfIIaAe0ib5Bqa2vz8vIqKytdH1ZWVnbjxg0fft3Wp9UBHqBGQHtJGqSjR48uWLAgNzd3+fLlv//9750dVl1dvWjRorKyMv9NwvIIPkGNgDbJ+I6xJpMpMzPzwIEDer2+oaFh4sSJqampcXFxdoc9ePDg9ddf79mzpw+/NJt18AlOqwM8IGOQTpw4ERkZqdfrhRBRUVHJycknT55sHaQtW7Y888wz5eXlzm7HYDBY/97m1p+gRvARagR4RsYgNTY2JiQkWC927dq1qqrK7pi//e1vJSUlhw4devnll53djjsRcoYawTPUCPCYjEEymUw63T8f3NLpdGaz2faA27dvZ2Rk7Nixw4dflHMZ4D1qBHhDxiCFhYWZTCbrRbPZHBoaanvAxo0bBw8eXFNTU1NT09DQUF5eHhsba7tB115s1sF71AjwkoxBio6OvnDhgvWi0WicOnWq7QG9evW6ePHivn37hBB1dXUFBQXdu3f3Jki2qBE8QI0A78kYpJEjRwohCgoKxo0bd/ny5eLi4nfffVcIUVZWFh0d3bdv31WrVlkPfvnll+fOnZuSkuLxl2OzDl6iRoBPyBgknU63efPm1atX6/X68vLy7Oxsy7ndOTk506ZNS0tL8+HXYrMOXuKl6gBf6dDS0qL0DH5hMBjae6o3NUJ78XIMgA9J+koNgcFmHbxBjQDfCuog2WJ5hHahRoDPBW+QWB7BY9QI8IcgDRLnMsBj1AjwkyANki1qBPdRI8B/ZDzt29/YrINneL4R4FfBvkJieQQ3USPA34I9SIA7qBEQAEG3ZcczYdEuPGgEBAwrJMApagQEUnAFidMZ4D5qBARYcAXJFvt1cIEaAYEXREFieQQ3USNAEUEUJFssj+AMNQKUEqRBAhyiRoCCguW0b/br4JrD99mjRkAgBUuQbLFfBzssjAAZsGWHYEeNAEkERZB4dQY4Q40AeQTjlh0geNAIkE9QrJAAO9QIkJD2V0icXwc7bNMBcgquFRIPIIEaAdLS/goJsGCbDpAcQUJQYGGkUjdu3NizZ8/Vq1fDw8Pnz58/cuRIpSeCH2k8SDyABC0tjC5evDh48GAPrlhXV/fII4907drV5yP5VVVV1fvvv5+ZmdmjR4+qqqof//jHr7322rvvvqv0XPCXIHoMiQeQgpCWarRjx46dO3d6dt2mpqbZs2ffuHHDtyP523vvvbdr1676+nohRHx8/OTJk7Oysm7fvq30XPAXeYNUW1ubl5dXWVnp7IDq6uq8vLy///3vgZwKKuJwm07CGp06dSoxMTEtLW3SpElFRUUOj9mzZ09eXt6WLVs8+xJ6vf7tt9+eNGnS3bt3vZg00AwGQ2hoaMeO/7uRo9PprP8LTerQ0tKi9AwOHD16dMOGDWPGjDlz5kxqauqqVavsDsjKysrPzx8xYkRVVVVERMTu3bvDwsJsDzAYDJWVlbxGQ3BS0cLo0qVLP/7xj7dt26bX6xcsWNCjR49z587ZHXPu3Llp06aVl5d3797dm6/1zjvvlJeXHzhwwJsbUVDfvn0TEhKOHz+u9CDwFxkfQzKZTJmZmQcOHNDr9Q0NDRMnTkxNTY2Li7MeUFFR8fHHHxcWiwd6LgAADVJJREFUFkZGRgohZsyYcfTo0bS0NMUmhkxUVCMhREZGRnNz88KFCxctWvTtt986fIjoueeee/vtt72skRAiPT194MCBhw4devbZZ728qcBbt25d7969//znPys9CPxIxiCdOHEiMjJSr9cLIaKiopKTk0+ePGkbpMjIyA8++MBSIyHEj370o2+/dfDrhuVRsFFXioQQDx8+PHTo0IABA0JDQzMyMgYMGNB6M+CPf/zjrVu3XnzxRe+/XGho6Jo1a954441Zs2apaOPr/fffP3PmTFVV1YYNG3r37q30OPAjGf9RNjY2JiQkWC927dq1qqrK9oC+ffuOGTPG8veamprjx49PmjQpoCNCPqqrkRDi2LFjJpPJcirzkCFDNmzY0LdvX7tjNm3atGzZMl/1Y8mSJbW1tfv37/fJrQXGypUrd+/e/eWXX65evXrhwoVKjwM/kjFIJpPJ9sdPp9OZzWaHR16/fn3JkiUrVqwYNGhQoKaDdLr9vxlqOX/BzqVLl4QQLp5bU1RUVFlZOXfuXF99xS5dukydOnXXrl2+usGACQ8PX7hw4b59+/bs2aP0LPAXGYMUFhZmMpmsF81ms/U0G1vnz5+fPXv2888/v3z58gBOB7mocWFk9dVXXwkh4uPjnR1w8ODBPn362G4YeG/KlCkFBQWqOHn617/+9Ycffmi9aNnGP3bsmHITwb9kfAwpOjr6woUL1otGo3Hq1Kl2xxQXF69atWrdunWTJ08O7HSQhXpT9Pnnnx88eFAIcfLkSSHEzp07P/74YyHEtm3b7J67mp+fP3bsWGe3YzQa33nnnerqaqPRmJKS8tZbb92/f3/t2rXXrl27c+fOsmXLHC6thg4dajKZ8vPzZ82a5eNvzD1ujn327NlNmzZ17tx52bJllis2NzcLIXr06KHI2AgAGYNk2cEoKCgYN27c5cuXi4uLLc/NLisri46O7tu3b21t7cqVK997772kpKQHDx4IIXQ6XUhIiMJzI1AcpkiopEZCiAEDBsyePdtsNn/00UfR0dHPP/+85eN2NXr48OHFixed/SfXjRs3FixY8Pvf/37IkCH3799/8sknb968ee3atbfffjshIWHp0qXz5s27du1av3797K5o+fn66quvFAmS+2MPGTIkJiZm9+7d1ut+8cUXYWFhv/jFLwI/NgJDxiDpdLrNmzevXr1ar9eXl5dnZ2f37NlTCJGTkzNt2rS0tLR9+/b94x//sP13uXDhwoyMDNsbqar65zNqOcVOS9S7MLIaPHjw4MGDS0pKhBBjx451FobS0lKTyTRs2DCHn12+fPkf/vAHy3ZfeHj4iBEjtm3blpWVNXz48IMHD+7bty8kJMThXndoaGjnzp2vXLniesiDBw8uXbq0fd+YEP/xH/8xc+ZMFwe4P3bHjh0PHTq0adOmu3fv9ujRo7y8/NixY4cPH/bsxZOgCjIGSQgxevTo1k9Zt/630po1a9asWRPwoaAwtS+M7FRXVwshDAaDswMsL5kTERHR+lPnzp3r06eP7YNPlmc+LFmyRAgxfvz45cuXT58+3dlJ0hEREbdu3XI93uzZs/v06dPmd2EnMTHRxWfbO/bo0aMPHDhQUFBw7dq1xx57rK6uLjQ0tL0jQUUkDRJgS2MpsrD8J5eLU+y+//57IYTDVU54ePirr75qvfjw4cOioqK4uDjLBl2vXr22b9/u4ks/+eSTLl6Uy6Jjx44uHr7yjAdj63S6CRMm+HYMSIsgQWqaTJGFZdPsqaeecnaA5dkODoNkd2JeXl6eyWRKTk5280vrdLr79++3Y1Yf8XJsaB5BgqScpUhookZCiBMnTnTu3Ll///7ODujUqZP4v1PLXCssLBRCTJkyxc0vXV9fP2DAADcP9p/2jg3NI0iQkYYXRhZ1dXVNTU0pKSkujunSpYsQoqmpqc1bO3HihBAiKSnJ+hGz2ezsCXxCiGvXrlme0+PCqVOntm7d2uaXtvPLX/7S9cNItto7NjSPOx5y0XyKLCyn2LlepowYMUL836kNdu7evVtaWmp5jOfhw4enTp2KiYmJjY21HrBjx44ePXrMnz/f4S3fvXv3kUcecT3hY4891vr5f2167LHHXHzWy7GheQQJsgiSFFmUlpYKIcaPH+/imF69ekVERJSVldl93Gw2jxo1qqKi4sCBA3Pnzv3000+tL4hn0dzcvHfvXmdv01BXV2cymdpcx8TGxi5evNid78VNXo6NYECQoDDNP1bkUHl5uXD5okEWU6ZMsbzenS2j0VhRUdGtW7ehQ4c2Nzdv3bo1OTn5+vXr1gNeeuml9PR0Z2dIWxZnluVXIHk5NoKBpG/Q5z3ee0J+wZkii6ioqPv379+7d8/1YR9++OGKFSvu3btn92t63rx5nTp1mjx58sGDB9esWRMXF/fTn/50/PjxQ4YMOXLkyNKlS128Huurr766f/9+2xIEjDdjIxhoM0i2NRIEST4uUiSCoEb19fUxMTGzZ88+dOiQ6yONRmPv3r337t3b+jd1VVVVdXX1+PHjLec+CCGKioru3LmTkpLi+qSAhISEmTNnbty40ZtvwWMej41goP0gUSOpBPOqyPK8Ip1Od+jQoTlz5vzpT3964YUX2rzWSy+9VFtb+8UXX/hkhpKSkqeffvrSpUttnmUHBB7/SYIACeYUCSEuXbo0bty4Ll26fPPNN//1X//VrVs3N88lS09Pj4+Pv3Tpkk/ehGLTpk0vvPACNYKcCBL8K8h356x27tz53XffxcXFCSGOHDmyZs2a8PBwd644YMCA3/72t7/5zW8OHz7s5Qxnz57Nz8+vqKjw8nYAP2HLDv5CimwdP358wYIFW7ZsuXjxYnFx8Zdffun+u5KbzeZx48atWLHiZz/7mccDNDc3/+QnP8nKynL9atyAgggSfMx1h0Twpcjq3Llzn376aVxc3OLFi92vkcWNGzdmzZq1detWj0/XXrx48ejRo1euXOnZ1YEAIEjwDTrkbzdv3szOzvbs7LhTp05VV1f79omugM8RJHilzQ4JUgTAPZzUAE/QIQA+R5DQDu50SJAiAB4hSGgbHQIQAAQJjrkZIUGHAPgIQcI/uR8hQYcA+BpBCnbtipCgQwD8hiAFIyIEQEIEKSi0t0AWdAhAIBEkDfIsPxZECIBSCJK6edMeKyIEQAYESR18Eh4rCgRAQioOUm1tbWVlZWxsrMFgUHoWb/m2N62pokAGg6GyslLpKdAO3GXqIv/9pdYgHT16dMOGDWPGjDlz5kxqauqqVauUnuif/F2XNqkiPwBgR5VBMplMmZmZBw4c0Ov1DQ0NEydOTE1NtbwXZ2uK58GvaA8AzVBlkE6cOBEZGanX64UQUVFRycnJJ0+edBYkbZhxvpvjT6h/u9KWBnZfgw13GXxIlUFqbGxMSEiwXuzatWtVVZXtAZb3eKpKiwnwYN5wvdaRet8XAHxBlUEymUy27wCt0+nMZrOC89hhGw0APKDKIIWFhZlMJutFs9kcGhra+jDCAAAqomv7EPlER0dfuHDBetFoNI4YMULBeQAA3lNlkEaOHCmEKCgoEEJcvny5uLg4MTFR6aEAAF7p0GI5AUBtSkpKVq9erdfry8vLs7KypkyZovREAACvqDVIAACNUeWWHQBAewgSAEAKqjztu01aet1VrXJxHzU0NFy5csV6MT4+vnv37oGdDm4pLCwcO3as0lPAFYf3kbQ/YhoMksyvuwoL1/fRp59+umXLlrCwMMvFrVu3JiUlKTEmXNm+ffv+/fsLCwuVHgROObuP5P0Ra9GWhw8fPvXUU5cvX25pabl58+awYcO++eYbpYfCD7R5H7322mt79+5VZji4wWg0/uY3v3nqqaeSkpKUngWOub6PpP0R09pjSA5fd1XpofADbd5HFy9e/Jd/+ZeGhoYHDx4oNCNcycnJiYqKWr9+vdKDwCnX95G0P2Ja27Jr83VXoTjX95HJZPrv//7vd999t6GhobGx8dlnn83KylJiTDiVkZGh0+ksz0yHnFzcRzL/iGlthST5665CtHUfXb9+PSUl5cMPPywuLj5+/HhhYeH+/fuVGBNO2d59kJOL+0jmHzGt/cNq/bqrHTtqbRWodq7vo5iYmK1bt8bExAghevfuPWnSpDNnzigwJaBRMv+IaS1IvO6q/FzfRzU1NZ988on1YnNzc0hISEDnAzRN5h8xrQWJ112Vn7P7qKysrL6+/v79+5mZmdXV1UKI69evf/nllzNmaPlN6IGAkf9HTGvbWTqdbvPmzdbXXc3Ozu7Zs6fSQ+EHnN1HOTk506ZNS0tL++1vfztv3ryhQ4eeP3/+3/7t32R5hgSgcvL/iGn2xVXv3bsXHh7Oo68yc3Efmc3m+/fvcw8CfiLnj5hmgwQAUBeJ2ggACGYECQAgBYIEAJACQQIASIEgAQCkQJAAAFIgSAAAKRAkAIAUCBIAQAoECQAgBYIEAJACQQIASIEgAQCkQJAAAFIgSAAAKRAkAIAUCBIAQAoECQAgBYIEAJACQQIASIEgAQCkQJAAAFIgSAAAKRAkAIAUCBIAQAr/H7AN8+5Bzf7tAAAAAElFTkSuQmCC\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43003,"title":"Simpsons's rule (but not Homer Simpson)","description":"I wonder what Homer Simpson would have thought of Simpson's rule? Somehow I doubt his thoughts would have included the phrase Newton-Cotes, or even numerical integration.\r\n\r\nIn this problem, I want you to use \u003chttps://en.wikipedia.org/wiki/Simpson%27s_rule Simpson's rule\u003e to integrate a function, provided as a list of points in a vector. The points must be equally spaced in x, so all that need be provided is the spacing between points in x. As well, I'll be nice and always give you an odd number of points, since that is important for Simpson's rule to work smoothly.\r\n\r\nAs a test case, we should know that the integral of cos(x) over the interval [0,pi/2] is 1, at least analytically that is true. Your Simpson's rule code, for only 7 points spanning that interval will do pretty well:\r\n\r\n deltax = pi/12;\r\n Fx = cos(linspace(0,pi/2,7));\r\n simpsInt(Fx,deltax)\r\n ans =\r\n 1.00002631217059\r\n\r\nThus, Fx is a vector of supplied function values, and deltax is the step size taken on the x-axis.\r\n\r\nHomer would be proud.","description_html":"\u003cp\u003eI wonder what Homer Simpson would have thought of Simpson's rule? Somehow I doubt his thoughts would have included the phrase Newton-Cotes, or even numerical integration.\u003c/p\u003e\u003cp\u003eIn this problem, I want you to use \u003ca href = \"https://en.wikipedia.org/wiki/Simpson%27s_rule\"\u003eSimpson's rule\u003c/a\u003e to integrate a function, provided as a list of points in a vector. The points must be equally spaced in x, so all that need be provided is the spacing between points in x. As well, I'll be nice and always give you an odd number of points, since that is important for Simpson's rule to work smoothly.\u003c/p\u003e\u003cp\u003eAs a test case, we should know that the integral of cos(x) over the interval [0,pi/2] is 1, at least analytically that is true. Your Simpson's rule code, for only 7 points spanning that interval will do pretty well:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003edeltax = pi/12;\r\nFx = cos(linspace(0,pi/2,7));\r\nsimpsInt(Fx,deltax)\r\nans =\r\n 1.00002631217059\r\n\u003c/pre\u003e\u003cp\u003eThus, Fx is a vector of supplied function values, and deltax is the step size taken on the x-axis.\u003c/p\u003e\u003cp\u003eHomer would be proud.\u003c/p\u003e","function_template":"function y = simpsInt(Fx,deltax)\r\n % simple Simpson's rule integration.\r\n y = Fx;\r\nend\r\n","test_suite":"%%\r\ndeltax = pi/12;\r\nFx = cos(linspace(0,pi/2,7));\r\ny_correct = 1.00002631217059;\r\ntol = 1e-14;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 0.125;\r\nFx = exp((0:8)/8);\r\ny_correct = 1.7182841546999;\r\ntol = 1e-14;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = (0:10).^2;\r\ny_correct = 1000/3;\r\ntol = 1e-11;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = (0:10).^4;\r\ny_correct = 20001.3333333333333;\r\ntol = 1e-9;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = sin(-5:5);\r\ny_correct = 0;\r\ntol = 1e-15;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 0.25;\r\nFx = sin(0:.25:100);\r\ny_correct = 0.13768413796203;\r\ntol = 1e-15;\r\nassert(abs(simpsInt(Fx,deltax) - y_correct) \u003c tol)\r\n\r\n%%\r\ndeltax = 1;\r\nFx = double((0:10) \u003e= 5);\r\ny_correct = 5.66666666666667;\r\ntol = 1e-14;\r\nabs(simpsInt(Fx,deltax) - y_correct) \u003c tol\r\n\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":9,"created_by":544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":"2016-10-02T01:31:18.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-01T23:16:52.000Z","updated_at":"2026-04-04T10:41:35.000Z","published_at":"2016-10-01T23:16:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI wonder what Homer Simpson would have thought of Simpson's rule? Somehow I doubt his thoughts would have included the phrase Newton-Cotes, or even numerical integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, I want you to use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Simpson%27s_rule\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSimpson's rule\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e to integrate a function, provided as a list of points in a vector. The points must be equally spaced in x, so all that need be provided is the spacing between points in x. As well, I'll be nice and always give you an odd number of points, since that is important for Simpson's rule to work smoothly.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs a test case, we should know that the integral of cos(x) over the interval [0,pi/2] is 1, at least analytically that is true. Your Simpson's rule code, for only 7 points spanning that interval will do pretty well:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[deltax = pi/12;\\nFx = cos(linspace(0,pi/2,7));\\nsimpsInt(Fx,deltax)\\nans =\\n 1.00002631217059]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThus, Fx is a vector of supplied function values, and deltax is the step size taken on the x-axis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHomer would be proud.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1031,"title":"Composite Trapezoidal Rule for Numeric Integration","description":"Use the trapezoidal rule to numerically integrate a function, _f(x)_, passed as the first argument, between upper and lower limits of integration, _x=a_ and _x=b_,passed as the second and third arguments, respectively. Use _n_ equal intervals, the optional fourth argument, for composite trapezoidal rule.","description_html":"\u003cp\u003eUse the trapezoidal rule to numerically integrate a function, \u003ci\u003ef(x)\u003c/i\u003e, passed as the first argument, between upper and lower limits of integration, \u003ci\u003ex=a\u003c/i\u003e and \u003ci\u003ex=b\u003c/i\u003e,passed as the second and third arguments, respectively. Use \u003ci\u003en\u003c/i\u003e equal intervals, the optional fourth argument, for composite trapezoidal rule.\u003c/p\u003e","function_template":"function I = trapezoidal_rule(f,a,b,n)\r\n% trap: composite trapezoidal rule quadrature\r\n% I = trap(f,a,b,n):\r\n% composite trapezoidal rule\r\n% input:\r\n% f = name of vectorized function to be integrated\r\n% a, b = integration limits\r\n% n = number of segments (default = 100)\r\n% output:\r\n% I = integral estimate\r\n\r\nend","test_suite":"%% Simple Trapezoidal Rule\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nassert(isequal(trapezoidal_rule(f,a,b,1),5280))\r\n\r\n%% Composite Trapezoidal Rule for 2 intervals\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nassert(isequal(trapezoidal_rule(f,a,b,2),2634))\r\n\r\n%% Composite Trapezoidal Rule for 4 intervals\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nassert(isequal(trapezoidal_rule(f,a,b,4),1516.875))\r\n\r\n%% Exact analytical comparison\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nP=polyint(p);\r\nI_correct=polyval(P,b)-polyval(P,a);\r\nI=trapezoidal_rule(f,a,b);\r\nassert(abs(I-I_correct)\u003c1)\r\n\r\n%% Exact analytical comparison--higher tolerance\r\np=[2 0 -4 0 -1 1];\r\na=-2;\r\nb=4;\r\nf = @(x) polyval(p,x);\r\nI = trapezoidal_rule(f,a,b,1000);\r\nP=polyint(p);\r\nI_correct=polyval(P,b)-polyval(P,a);\r\nassert(abs(trapezoidal_rule(f,a,b,1000)-I_correct)\u003c1e-1)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":279,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":114,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-11-13T19:14:48.000Z","updated_at":"2026-04-04T10:48:38.000Z","published_at":"2012-11-13T20:00:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUse the trapezoidal rule to numerically integrate a function,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, passed as the first argument, between upper and lower limits of integration,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex=b\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e,passed as the second and third arguments, respectively. Use\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e equal intervals, the optional fourth argument, for composite trapezoidal rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":47874,"title":"Compute an integral of an exponential function","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 125px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 62.5px; transform-origin: 407px 62.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.3583px 7.91667px; transform-origin: 72.3583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis problem builds on \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/47673-area-under-standard-normal-curve\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 47673\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 225.583px 7.91667px; transform-origin: 225.583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, in which Mehmet OZC asks us to compute the area under the standard normal curve. Write a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 131px; height: 44px;\" width=\"131\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.8083px 7.91667px; transform-origin: 53.8083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = IntegralExpFn(a,b,p)\r\n y = f(a,b,p);\r\nend","test_suite":"%%\r\na = log(2); b = 1; p = 1;\r\ny_correct = 1/2;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = Inf; b = 1; p = 1;\r\ny_correct = 1;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = Inf; b = 1; p = 2;\r\ny_correct = sqrt(pi)/2;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = 3; b = 1; p = 3;\r\ny_correct = 0.8929795115691813;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = 1; b = 1/2; p = 1.5;\r\ny_correct = 0.8278055502117507;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = Inf; b = randi(10); p = 1/2;\r\ny_correct = 2/b^2;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\na = 0; b = 4; p = 7/2;\r\ny_correct = 0;\r\nassert(abs(IntegralExpFn(a,b,p)-y_correct) \u003c 1e-14)\r\n\r\n%%\r\nfiletext = fileread('IntegralExpFn.m');\r\nillegalfns = ~isempty(strfind(filetext, 'integral')) || ~isempty(strfind(filetext, 'quad')); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-10T04:36:31.000Z","updated_at":"2026-01-09T17:40:58.000Z","published_at":"2020-12-10T05:15:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem builds on \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/47673-area-under-standard-normal-curve\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 47673\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, in which Mehmet OZC asks us to compute the area under the standard normal curve. Write a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = \\\\int_0^a \\\\exp(-b x^p) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr/\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":50509,"title":"Find the area between curves (P4)","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 601px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 300.5px; transform-origin: 407px 300.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 3px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 3px; outline-color: rgb(60, 60, 60); perspective-origin: 384px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); transform-origin: 384px 10px; white-space: pre-wrap; margin-left: 4px; margin-top: 3px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eArea between curves - Problem 4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFind the area enclosed by the curves \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAmCAYAAAAFkDNCAAAFP0lEQVR4Xu2aeah1UxjGf59ZohAiRUoSGTJGooiQeR6Tec5M5nmeSxkSZQ6ZUsos/iD+MCX8Yc4YmZJZP73ra939nWHve0/nnrPP2nXrdu/ae6/3Xc963ud91p5DuUoGsgzMKdkoGcgzUABR8DAlAwUQBRAFEAUD3TNQGKKgozDEDDGwOXAJcAjw/gyfNXK3F4ZotiTLALcAqwB7FUA0S17bRs8PnACcBnxZANG25W0ez/rAPsDfwNYFEM0T2KY7lgSuBK4Fdgd2K4Bo0/I2i0WddSjwG3APcHYBRLMEtm30WsCRwBnAT8A5BRBtW+L68SwGXAzcAbwVtxVA1M9fq0ZaKvYDlgZuBP4tgGjV+jYOZlXgeuBO4Nvs7n2BLYALgE+AN4GfGz99RG8oxlT3hdkUeLnPugmGVhlUvQBh/dwA2AXYBtClOwh4IpK0OHAqcAzwNHBcZSeN0h5wrsayLqCfsFrs7GOBX7OJCoLbQy8Yz9cdghg3DWHJ0z/ZEngXWA54AVgz1va6cF//D7UXIFaMZPwJXAUcANwVAPgHuAxYFNgI+B44EPi0DwpciAeAtWeIlnOBixo8YwFAUCwBnAUcFm7jzsBr2XO2B+6LsXvHXKuvGRdAGPMeEa8510MR/AuHp3J85GAH4I0UZN2ScQRwc9woMHzI55G8JLbqrM9sASKf28rA3YBs4OJ6UJVimA/YFrgpQCPzjSMgXPSTgEujXb4G+CsLxLgvBB4Kj+XHpoBYL0rF8kEv3wHnV15SBxCjMMYzifMCDE8F8xlPuiyN7iYNKEXjuF0yw8nA5cBtwImVsrhQ/M+/K4z9mbup6zLECuHSqa6fjyR+MW6ZyuZrPX0E+CXYbi5lAhsCewbV/j6gGNOOnO7jmohXz1nc+TK4ZS/5J+nd2vCWfsvjTsDj+aTqAmIRQNo5GlCE6Nr9Md3oRuC+HOC6kB5pe8ke6pOXgGcHOM9hAWLZYIUdo1zIhHmpMKTE9t906pDqAsJxdhRXAJ1odoC5G8qjctoUDNKnZxVqHEF/ZoVmhzKpAbxkV+DhLoI5Ad7je7VFahCmeCh1AWGrJg2tBHwYJ35VKqoTzyiIyjRPXUjFpS2Yv7tj1EWWxEGyQ528DGKMHZ/sbQNgOfSLrh8qD87zr+h0/JSrDiDsW28Ir+FgYBNg/9AUTQMZJUAk6lRHeKRtW6rJdHqwRdPYZnt8Xga1BCxTfruRLjsPOyoFp5daY54uqh8gVKxSzMfAY6EjRGB6oX7EZvEpWScTZ7aT1Ov9dhP3AluF4WYbeivw+ihPusfc8s1W9WlcZ80pvSLNuc9CcPrll3HLivpN8xhT3qh5I7I0MXzIxtmuSX5E0hFrBNLsaQelyIe1HrlQNjHSp+1mvquGNZdBvCdniFwX6a14/rI68FGITsu/DrOekhvgxTSBKkOsAzwKLAV8EM7jUZmFa0vm//UjZAzpVgoaN3ZI8SsmBcGTYdB8NYiVmaVnyOZ6CgpihaIHcy62bqVfh9slnhKG1CuxZg+GG9vVh1AveKNty/3RguVJUrjYykg9soS/Sz/jeikmteXVRM+NaxDZvNVBblDPnLyeibOZVwHLu+DQcfZMIwnoKU5zPw3Rghx1DcHYZYgFYxNU+/U2x94zKRMZeJx6Hh406qdx5epz2tnmBFkabcEsj++1OdCmsU1CyTBGuyG7ircBv/PQa9Cpe6dpwto+fhIAIRhU07ZdOni20yrw/ECr7etcO75JAEQ6zt4uvp6+Ghjn9rL24k5n4CQAYjp5mdh7CiAmduk7B/4fkkIVNjyeyg0AAAAASUVORK5CYII=\" width=\"66\" height=\"19\" style=\"width: 66px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"67\" height=\"18\" style=\"width: 67px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e for different \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ea\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eb\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ec\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e coefficients\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e Plot of curves for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"18\" style=\"width: 126px; height: 18px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = AreaCurves(a, b, c)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('AreaCurves.m');\r\nfor ii = [6.5065, 6.3475, 0.1134, 9.4710, 4.0104]\r\n assert(isempty(strfind(filetext, num2str(ii))),'Do NOT use provided answers in your solution')\r\nend\r\nassert(isempty(strfind(filetext, 'if')),'if: Forbidden')\r\nassert(isempty(strfind(filetext, 'switch')),'switch: Forbidden')\r\n%%\r\na = 1;\r\nb = 1;\r\nc = -2;\r\n\r\ny_correct = 6.5065;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 1;\r\nb = 2.5;\r\nc = -5; \r\n\r\ny_correct = 6.3475;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 0;\r\nb = 4.8;\r\nc = -0.5; \r\n\r\ny_correct = 0.1134;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = pi;\r\nb = pi;\r\nc = -pi;\r\n\r\ny_correct = 9.4710;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n%%\r\na = 2;\r\nb = 70;\r\nc = -6;\r\n\r\ny_correct = 4.0104;\r\nassert(abs(AreaCurves(a,b,c)-y_correct)\u003c1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":1,"created_by":487522,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-02-20T22:13:12.000Z","updated_at":"2026-01-18T15:37:37.000Z","published_at":"2021-02-20T22:13:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eArea between curves - Problem 4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the area enclosed by the curves \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = y^4 - a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58394,"title":"Integrate a product of gamma functions","description":"Write a function to compute the following integral:\r\n\r\nwhere and is the gamma function, the subject of Cody Problem 46025.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.1px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52.05px; transform-origin: 407px 52.05px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.742px 8px; transform-origin: 152.742px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 196.5px; height: 44px;\" width=\"196.5\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.55px; text-align: left; transform-origin: 384px 10.55px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 56px; height: 20px;\" width=\"56\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 29.5px; height: 18.5px;\" width=\"29.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 117.842px 8px; transform-origin: 117.842px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the gamma function, the subject of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/46025\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody Problem 46025\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intGammaProduct(a)\r\n f = @(x) gamma(1+i*a*x)*gamma(1-i*a*x);\r\n y = trapz(x,f);\r\nend","test_suite":"%%\r\na = tan(1);\r\nI_correct = 1.008596722571773;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sqrt(2);\r\nI_correct = 1.110720734539592;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = log(3);\r\nI_correct = 1.429800433690064;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = exp(4);\r\nI_correct = 0.028770138289325;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = sinh(5);\r\nI_correct = 0.021168845856719;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)\r\n\r\n%%\r\na = asinh(6);\r\nI_correct = 0.630391294450658;\r\nassert(abs(intGammaProduct(a)-I_correct)\u003c1e-13)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-06-03T19:50:53.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-06-03T14:18:04.000Z","updated_at":"2026-01-26T04:29:04.000Z","published_at":"2023-06-03T14:18:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_{-\\\\infty}^\\\\infty \\\\Gamma(1+iax)\\\\Gamma(1-iax) dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei = \\\\sqrt{-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\Gamma(z)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the gamma function, the subject of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/46025\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody Problem 46025\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":51137,"title":"Compute an integral of a product of sinusoids","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 52px; transform-origin: 407px 52px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150.8px 7.91667px; transform-origin: 150.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the following integral\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\" style=\"width: 139px; height: 44px;\" width=\"139\" height=\"44\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 7.91667px; transform-origin: 21.0083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003em\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96.5917px 7.91667px; transform-origin: 96.5917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are integers. You may not use \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.8px 7.91667px; transform-origin: 30.8px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.1083px 7.91667px; transform-origin: 10.1083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.4px 7.91667px; transform-origin: 15.4px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003equad\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.1917px 7.91667px; transform-origin: 99.1917px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but other functions are allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = intSinmCosn(m,n)\r\n y = f(m,n);\r\nend","test_suite":"%%\r\nm = 1;\r\nn = 0;\r\ny_correct = 2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 2;\r\ny_correct = pi/2;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 2;\r\ny_correct = 2/3;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 2;\r\ny_correct = pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 2;\r\ny_correct = 4/15;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 4;\r\ny_correct = 3*pi/8;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 4;\r\ny_correct = 2/5;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 4;\r\ny_correct = pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 4;\r\ny_correct = 4/35;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 4;\r\ny_correct = 3*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 4;\r\ny_correct = 16/315;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 4;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 4;\r\ny_correct = 32/1155;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 6;\r\ny_correct = 5*pi/16;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 6;\r\ny_correct = 2/7;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 6;\r\ny_correct = 5*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 6;\r\ny_correct = 4/63;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 6;\r\ny_correct = 3*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 6;\r\ny_correct = 16/693;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 6;\r\ny_correct = 5*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 6;\r\ny_correct = 32/3003;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 0;\r\nn = 8;\r\ny_correct = 35*pi/128;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 8;\r\ny_correct = 2/9;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2;\r\nn = 8;\r\ny_correct = 7*pi/256;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 3;\r\nn = 8;\r\ny_correct = 4/99;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 4;\r\nn = 8;\r\ny_correct = 7*pi/1024;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 5;\r\nn = 8;\r\ny_correct = 16/1287;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 6;\r\nn = 8;\r\ny_correct = 5*pi/2048;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 7;\r\nn = 8;\r\ny_correct = 32/6435;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 2*randi(9);\r\nn = m+1;\r\ny_correct = 0;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 22;\r\ny_correct = 2/23;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nm = 1;\r\nn = 28;\r\ny_correct = 2/29;\r\nassert(abs(intSinmCosn(m,n)-y_correct)\u003c1e-12)\r\n\r\n%%\r\nfiletext = fileread('intSinmCosn.m');\r\nillegalfns = ~isempty(strfind(filetext, 'integral')) || ~isempty(strfind(filetext, 'quad')); \r\nassert(~illegalfns,'Please do not use integral or quad')","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-03-23T00:29:43.000Z","updated_at":"2026-02-22T14:27:23.000Z","published_at":"2021-03-23T00:33:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the following integral\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = integral(sin(x)^m cos(x)^n, {x,0,pi})\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = \\\\int_0^\\\\pi \\\\sin^mx\\\\cos^nxdx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"m\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003em\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are integers. You may not use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003equad\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e but other functions are allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58997,"title":"Compute the water table elevation in an unconfined aquifer with recharge","description":"Problem statement\r\nWrite a function to compute the water table elevation above the bottom of the aquifer and the position of a groundwater divide given the water table elevations at , at , hydraulic conductivity , and recharge rate . If there is no groundwater divide, set xd to the empty set []. \r\nBackground\r\nAs in other problems in this series, the movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\r\n\r\nwhere is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position is \r\n\r\nwhere is the (unknown) flow at . Using Darcy’s law to replace provides a differential equation that can be integrated using the water table elevations at the boundaries to determine and a constant of integration.\r\nUnlike the flows in Cody Problem 58966, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 838.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 419.25px; transform-origin: 407px 419.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 164.792px 8px; transform-origin: 164.792px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the water table elevation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 206.542px 8px; transform-origin: 206.542px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15\" height=\"20\" alt=\"xd\" style=\"width: 15px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 101.917px 8px; transform-origin: 101.917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e given the water table elevations \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"15.5\" height=\"20\" alt=\"h0\" style=\"width: 15.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"17\" height=\"20\" alt=\"hL\" style=\"width: 17px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 8px; transform-origin: 9.71667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.35px 8px; transform-origin: 72.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, hydraulic conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.0667px 8px; transform-origin: 61.0667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and recharge rate \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"12\" height=\"20\" alt=\"i0\" style=\"width: 12px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27.6px 8px; transform-origin: 27.6px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. If there is no groundwater divide, set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003exd\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.6583px 8px; transform-origin: 53.6583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to the empty set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 8px; transform-origin: 7.7px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003e[]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 40.8333px 8px; transform-origin: 40.8333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35.3917px 8px; transform-origin: 35.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs in other \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eproblems\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/55825\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ein\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/56205\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003ethis\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eseries\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 264.883px 8px; transform-origin: 264.883px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91.5\" height=\"35\" alt=\"Q = -K(dh/dx)hw\" style=\"width: 91.5px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ew\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 333.967px 8px; transform-origin: 333.967px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.94167px 8px; transform-origin: 8.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" alt=\"Q = Q0 + i0 w x\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 77.4px 8px; transform-origin: 77.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the (unknown) flow at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 94px 8px; transform-origin: 94px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Using Darcy’s law to replace \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 135.633px 8px; transform-origin: 135.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"19\" height=\"20\" alt=\"Q0\" style=\"width: 19px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.1833px 8px; transform-origin: 92.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and a constant of integration.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 58.35px 8px; transform-origin: 58.35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eUnlike the flows in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 233.383px 8px; transform-origin: 233.383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 403.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 201.85px; text-align: left; transform-origin: 384px 201.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"586\" height=\"398\" style=\"vertical-align: baseline;width: 586px;height: 398px\" 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\" alt=\"Unconfined aquifer with recharge\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0)\r\n h = (h0+hL)/2;\r\n xd = x;\r\nend","test_suite":"%%\r\nL = 10; % Length (m) \r\nx = L/2; % Position where WTE is desired (m)\r\nh0 = 19.11; % Water table elevation at x = 0 (m)\r\nhL = 19.11; % Water table elevation at x = L (m)\r\nK = 5e-7; % Hydraulic conductivity (m/s)\r\ni0 = 6.9e-8; % Recharge rate (m/s)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = 19.2;\r\nxd_correct = 5;\r\nassert(abs(h-h_correct)\u003c1e-3)\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1200; % Length (m) \r\nx = 0:300:1200; % Positions where WTE is desired (m)\r\nh0 = 25; % Water table elevation at x = 0 (m)\r\nhL = 23; % Water table elevation at x = L (m)\r\nK = 4; % Hydraulic conductivity (m/d)\r\ni0 = 2e-4; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 24.789 24.393 23.801 23.000];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 1200; % Length (m) \r\nx = 0:300:1200; % Positions where WTE is desired (m)\r\nh0 = 25; % Water table elevation at x = 0 (m)\r\nhL = 23; % Water table elevation at x = L (m)\r\nK = 4; % Hydraulic conductivity (m/d)\r\ni0 = 8e-4; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [25.000 25.593 25.475 24.637 23.000];\r\nxd_correct = 400;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500; % Length (m) \r\nx = [100 200 300 700 1200 1800 2400]; % Positions where WTE is desired (m)\r\nh0 = 35; % Water table elevation at x = 0 (m)\r\nhL = 33.5; % Water table elevation at x = L (m)\r\nK = 50; % Hydraulic conductivity (m/d)\r\ni0 = 1e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [35.010 35.014 35.012 34.949 34.74 34.296 33.633];\r\nxd_correct = 222.5;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 2500; % Length (m) \r\nx = [100 200 300 700 1200 1800 2400]; % Positions where WTE is desired (m)\r\nh0 = 35; % Water table elevation at x = 0 (m)\r\nhL = 33.5; % Water table elevation at x = L (m)\r\nK = 60; % Hydraulic conductivity (m/d)\r\ni0 = 1e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [34.998 34.992 34.981 34.889 34.665 34.235 33.621];\r\nxd_correct = 17;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 20; % Length (m) \r\nx = 0:4:20; % Positions where WTE is desired (m)\r\nh0 = 5; % Water table elevation at x = 0 (m)\r\nhL = 3.5; % Water table elevation at x = L (m)\r\nK = 0.5; % Hydraulic conductivity (m/d)\r\ni0 = 1e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 4.752 4.482 4.188 3.864 3.5];\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(isempty(xd))\r\n\r\n%%\r\nL = 20; % Length (m) \r\nx = 0:4:20; % Positions where WTE is desired (m)\r\nh0 = 5; % Water table elevation at x = 0 (m)\r\nhL = 3.5; % Water table elevation at x = L (m)\r\nK = 0.1; % Hydraulic conductivity (m/d)\r\ni0 = 5e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nh_correct = [5 5.065 4.97 4.706 4.243 3.5];\r\nxd_correct = 3.625;\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\nassert(abs(xd-xd_correct)\u003c1e-3)\r\n\r\n%%\r\nL = 1000*rand; % Length (m) \r\nx = L/17; % Positions where WTE is desired (m)\r\nh0 = randi(100); % Water table elevation at x = 0 (m)\r\nhL = h0; % Water table elevation at x = L (m)\r\nK = 5; % Hydraulic conductivity (m/d)\r\ni0 = 5e-3; % Recharge rate (m/d)\r\n[h,xd] = unconfWithRecharge(x,L,h0,hL,K,i0);\r\nassert(abs(xd-L/2)\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('unconfWithRecharge.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-23T13:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-23T01:49:39.000Z","updated_at":"2026-02-12T13:52:11.000Z","published_at":"2023-09-23T01:49:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the water table elevation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e above the bottom of the aquifer and the position of a groundwater divide \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"xd\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_d\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e given the water table elevations \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, hydraulic conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and recharge rate \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"i0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ei_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there is no groundwater divide, set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003exd\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to the empty set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs in other \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eproblems\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/55825\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ein\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/56205\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethis\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eseries\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ethe movement of groundwater is governed by conservation of mass and (if the flow is slow enough) Darcy’s law. In an unconfined aquifer, the latter relates the flow of water to the gradient in water table elevation above the bottom of the aquifer by\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -K(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K\\\\frac{dh}{dx}hw\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"w\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ew\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the aquifer. For steady, one-dimensional flow, conservation of mass says that the flow at any position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = Q0 + i0 w x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = Q_0 + i_0 w x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the (unknown) flow at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Using Darcy’s law to replace \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e provides a differential equation that can be integrated using the water table elevations at the boundaries to determine \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and a constant of integration.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUnlike the flows in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, the flows here can have a groundwater divide, or a point in the profile that separates flow to the left from flow to the right. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" 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Sequences 115: Integral involving square root, floor, and round functions","description":"Given a postive real number , we are asked to evaluate the following integral:\r\n \r\n where: the symbol \"\" is the floor function,\r\n and \"\" is the round (to the nearest integer) function.\r\nWe may rewrite the above function in Matlab as:\r\n\u003e\u003e S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\r\nTherefore, for , we have:\r\n\u003e\u003e s = S(10*pi)\r\ns =\r\n 12\r\nBe careful though, in using the Matlab integral function, as it is only an approximation. For example if :\r\n\u003e\u003e s = S(100000)\r\n\r\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\r\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\r\nrequested accuracy. \r\n\u003e In integralCalc/iterateScalarValued (line 372)\r\nIn integralCalc/vadapt (line 132)\r\nIn integralCalc (line 75)\r\nIn integral (line 87)\r\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \r\n\r\ns =\r\n 49841\r\nThe correct answer is . The integral function is off by only 2 units here, but the discrepancy could be even greater for other values of . integral function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 673px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 445.71875px 336.5px; transform-origin: 445.71875px 336.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-18px\"\u003e\u003cimg 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\" 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src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/round.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eround \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(to the nearest integer) function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe may rewrite the above function in Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 30px; transform-origin: 442.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; s = S(10*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBe careful though, in using the Matlab \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/integral.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efunction, as it is only an approximation. For example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"18\" style=\"width: 74px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 260px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 130px; transform-origin: 442.71875px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt; s = S(100000)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eWarning: Reached the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003elimit on the maximum number of intervals in use. Approximate bound on error is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e8.0e+01. The integral \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003emay not exist\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e, or \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eit may be difficult to approximate numerically to the\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erequested \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eaccuracy. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt; In integralCalc/iterateScalarValued (line 372)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc/vadapt (line 132)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc (line 75)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegral (line 87)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e@(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e 49841\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe correct answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"18\" style=\"width: 65px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n % NOTE: the following expression is inaccurate for some values of n\r\n s = round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n)); \r\nend","test_suite":"%%\r\nn = 1:20;\r\ns_correct = [0 0 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7 7];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:20).*pi;\r\ns_correct = [1 2 3 4 6 7 8 11 11 12 15 16 17 18 20 22 23 24 26 28];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100*exp(1);\r\ns_correct = 126;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 1234.5678;\r\ns_correct = 601;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 12345.6789;\r\ns_correct = 6125;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100000;\r\ns_correct = 49839;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 6e6;\r\ns_correct = 2998571;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 4e8*pi;\r\ns_correct = 628304194;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 10.^(1:10);\r\ns_correct = 5555500618;\r\nassert(isequal(sum(arrayfun(@S,n)),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:1e5).*exp(2);\r\ns = arrayfun(@S,n);\r\nss = round([sum(s) nnz(s) mean(s) median(s) mode(s) std(s) sum(num2str(s))]);\r\nss_correct = [18444149135 100000 184441 184439 303161 106553 37072130];\r\nassert(isequal(ss,ss_correct))\r\nassert(isempty(lastwarn))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-18T18:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-05-18T18:10:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-04T18:21:04.000Z","updated_at":"2023-05-18T18:10:26.000Z","published_at":"2023-05-05T19:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=S(n)=\\\\Bigg\\\\lfloor\\\\ \\\\int_0^n\\\\sqrt{\\\\lfloor{x}\\\\rfloor} - \\\\Big\\\\lfloor{\\\\sqrt{x} \\\\Big\\\\rfloor\\\\ \\\\mathrm{d}x\\\\ \\\\Bigg\\\\rceil \\\\cdot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e where: the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/round.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eround \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e(to the nearest integer) function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe may rewrite the above function in Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e s = S(10*pi)\\ns =\\n 12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBe careful though, in using the Matlab \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/integral.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003efunction, as it is only an approximation. For example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=100000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e s = S(100000)\\n\\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\\nrequested accuracy. \\n\u003e In integralCalc/iterateScalarValued (line 372)\\nIn integralCalc/vadapt (line 132)\\nIn integralCalc (line 75)\\nIn integral (line 87)\\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \\n\\ns =\\n 49841]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correct answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=49839\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":59029,"title":"Compute the water table in a layered unconfined aquifer","description":"Write a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at and , and the length of the aquifer.\r\nBackground \r\nCody Problem 52070 dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \r\nFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE varies with , so does :\r\n\r\nThen using Darcy’s law as in Cody Problem 58966, one can write the flow through the aquifer as\r\n\r\nConservation of mass says that in steady one-dimensional flow, the flow past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions and to determine the flow and the constant of integration. \r\n\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 836.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 418.15px; transform-origin: 407px 418.15px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 367.442px 8px; transform-origin: 367.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"39\" height=\"18\" alt=\"x = L\" style=\"width: 39px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and the length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eL\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3333px 8px; transform-origin: 44.3333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of the aquifer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.775px 8px; transform-origin: 42.775px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eBackground \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 85px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42.5px; text-align: left; transform-origin: 384px 42.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 52070\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 306.625px 8px; transform-origin: 306.625px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 330.125px 8px; transform-origin: 330.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 321.408px 8px; transform-origin: 321.408px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 36.95px 8px; transform-origin: 36.95px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e varies with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13.2167px 8px; transform-origin: 13.2167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, so does \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"24.5\" height=\"20\" alt=\"Keff\" style=\"width: 24.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"172\" height=\"35\" alt=\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\" style=\"width: 172px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.8917px 8px; transform-origin: 90.8917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThen using Darcy’s law as in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 58966\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.5083px 8px; transform-origin: 73.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, one can write the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 70.0167px 8px; transform-origin: 70.0167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e through the aquifer as\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 34.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 17.4px; text-align: left; transform-origin: 384px 17.4px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"183\" height=\"35\" alt=\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\" style=\"width: 183px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 64px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32px; text-align: left; transform-origin: 384px 32px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 224.825px 8px; transform-origin: 224.825px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.058px 8px; transform-origin: 152.058px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"61\" height=\"20\" alt=\"h(0) = h0\" style=\"width: 61px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 8px; transform-origin: 15.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64.5\" height=\"20\" alt=\"h(L) = hL\" style=\"width: 64.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0.991667px 8px; transform-origin: 0.991667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to determine the flow \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eQ\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.9583px 8px; transform-origin: 99.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and the constant of integration. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 346.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 173.35px; text-align: left; transform-origin: 384px 173.35px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"559\" height=\"341\" style=\"vertical-align: baseline;width: 559px;height: 341px\" 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alt=\"unconfined aquifer with soils in parallel\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L)\r\n% h = water table elevation above the aquifer bottom\r\n% Qp = flow per unit width\r\n% x = locations where WTE is requested\r\n% K1 = hydraulic conductivity of upper layer\r\n% K2 = hydraulic conductivity of lower layer\r\n% b2 = thickness of lower layer\r\n% h0 = water table elevation on the left side (x = 0)\r\n% hL = water table elevation on the right side (x = L)\r\n% L = length of the aquifer\r\n\r\n Qp = mean([K1 K2])*(h0-hL)*b2/L;\r\n h = h0 + (hL-h0)*x/L;","test_suite":"%%\r\nx = [0 251.884 503.2297 754.0371 1004.3062 1254.0371 1503.2297 1751.884 2000];\r\nK1 = 900; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 8000; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37; % Water table elevation on the left side (m)\r\nhL = 33; % Water table elevation on the right side (m)\r\nL = 2000; % Length of aquifer (m)\r\nb2 = 25; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 418;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 284.1463 558.5366 823.1707 1078.0488 1323.1707 1558.5366 1784.1463 2000];\r\nK1 = 8000; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 900; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 37; % Water table elevation on the left side (m)\r\nhL = 33; % Water table elevation on the right side (m)\r\nL = 2000; % Length of aquifer (m)\r\nb2 = 25; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 37:-0.5:33;\r\nQp_correct = 205;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 230.8945 460.1048 687.631 913.4731 1137.631 1360.1048 1580.8945 1800];\r\nK1 = 4; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50; % Water table elevation on the left side (m)\r\nhL = 48; % Water table elevation on the right side (m)\r\nL = 1800; % Length of aquifer (m)\r\nb2 = 16; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 0.1484;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 225.2925 450.5015 675.6269 900.6686 1125.6269 1350.5015 1575.2925 1800];\r\nK1 = 0.1; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 4; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 50; % Water table elevation on the left side (m)\r\nhL = 48; % Water table elevation on the right side (m)\r\nL = 1800; % Length of aquifer (m)\r\nb2 = 16; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 50:-0.25:48;\r\nQp_correct = 7.48e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7; % Water table elevation on the left side (m)\r\nhL = 2.8; % Water table elevation on the right side (m)\r\nL = 20; % Length of aquifer (m)\r\nb2 = 1.5; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 2.6558 5.2033 7.6423 9.9729 12.1951 14.3089 16.3144 18.2114 20];\r\nK1 = 0.5; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.1; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7; % Water table elevation on the left side (m)\r\nhL = 2.8; % Water table elevation on the right side (m)\r\nL = 20; % Length of aquifer (m)\r\nb2 = 1.5; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.613e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = [0 2.3183 4.6126 6.8829 9.1291 11.3514 13.5495 15.7237 17.8739 20];\r\nK1 = 0.1; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 0.5; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 3.7; % Water table elevation on the left side (m)\r\nhL = 2.8; % Water table elevation on the right side (m)\r\nL = 20; % Length of aquifer (m)\r\nb2 = 1.5; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = 3.7:-0.1:2.8;\r\nQp_correct = 4.163e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nx = 0:325:1300;\r\nK1 = 5; % Hydraulic conductivity of upper layer (m/d)\r\nK2 = 5; % Hydraulic conductivity of lower layer (m/d)\r\nh0 = 10; % Water table elevation on the left side (m)\r\nhL = 9; % Water table elevation on the right side (m)\r\nL = 1300; % Length of aquifer (m)\r\nb2 = 4; % Thickness of lower layer (m)\r\n[h,Qp] = unconfParallel(x,K1,K2,b2,h0,hL,L);\r\nh_correct = [10 9.7596 9.5131 9.2601 9];\r\nQp_correct = 3.65e-2;\r\nassert(abs(Qp-Qp_correct)\u003c1e-3)\r\nassert(all(abs(h-h_correct)\u003c1e-3))\r\n\r\n%%\r\nfiletext = fileread('unconfParallel.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'regexp'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-30T19:04:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-30T15:05:42.000Z","updated_at":"2023-09-30T19:04:22.000Z","published_at":"2023-09-30T15:09:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the flow per unit width and the elevation of the water table above the bottom of unconfined aquifer with two soil layers. The input to the function will be the positions where the water table elevation (WTE) is requested, the hydraulic conductivities of the two layers, the thickness of the bottom layer, the WTEs at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and the length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"L\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e of the aquifer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBackground \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/52070-compute-the-effective-conductivity-of-a-heterogeneous-aquifer?s_tid=ta_cody_results\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 52070\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e dealt with the effective conductivity of a heterogeneous confined aquifer. In that case, the effective conductivity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e for the case of flow through soil units in parallel could be computed by realizing that the head difference is same for the two soils and the total flow is the sum of the flows through the soils. The effective conductivity then is the weighted average of the individual conductivities, using the layer thicknesses as weights. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor an unconfined aquifer, the effective conductivity is computed in a similar way, but because the WTE \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e varies with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, so does \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Keff = (1/h)[(K2-K1) b2 + K1(h-b2)]\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK_{eff} = \\\\frac{1}{h}[K_2 b_2 + K_1(h-b_2)]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThen using Darcy’s law as in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/58966-compute-the-head-for-steady-1d-flow-in-a-homogeneous-aquifer\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 58966\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, one can write the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e through the aquifer as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q = -Keff(dh/dx)A = -Keff(dh/dx)hw\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ = -K_{eff} \\\\frac{dh}{dx} A = -K_{eff} \\\\frac{dh}{dx} h w\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConservation of mass says that in steady one-dimensional flow, the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e past any section is constant. Then the WTE can be computed by inserting the effective conductivity, integrating, and using the boundary conditions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(0) = h0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(0) = h_0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h(L) = hL\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh(L) = h_L\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to determine the flow \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"Q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and the constant of integration. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"341\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"559\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" 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Sequences 110: Integration of the Sum of a Recursive Trigonometric Function","description":"A trigonometric function, , is defined as follows:\r\n , in radians\r\nApplying recursively we define another function , for integer :\r\n \r\nWe then define as the sum of value of from to :\r\n \r\nFinally, we are asked to evaluate the integral of with respect to , over the real range :\r\n \r\nFor example for , , , we have:\r\n \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\r\n a = 7.05797686912156\r\nPlease present the final output rounded-off to 6 decimal places. Therefore the final answer is .\r\n-------------------------\r\nNOTE: There are a number of ways to do numerical Integration in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the integral function shown above.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 507px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 462.578125px 253.5px; transform-origin: 462.578125px 253.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA trigonometric function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"19\" style=\"width: 137.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in radians\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eApplying \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e recursively we define another function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAmCAYAAABJVvz/AAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAXKADAAQAAAABAAAAJgAAAADSajFxAAAGOUlEQVRoBe2YaWxWRRSGqaKiuKIxAbXSSkoMiYJEDSoVYl3igjEKajHGhRoNKmr0p4BGjBui8Y+BlF9AgibuSzQVtSb4QwE1EjVsNVhF0SDiRpHq+5R7kmE6d77v3n61S+6bvJ0z55zZzp05M1+HDClQRKCIQBGBIgJFBIoIDIgINGqWm8UjBsRs95/kTFVXizX7q+O1Ks98iuojPJ1b/VeVHWK7+LdryCHPVpvnxCaxOUf7vm4yVBN4VTxTnCRuEjNjvlpsFQlsKf4sHwa8XjxAzIKz5dwhLsjSqB/6Hq45rRXXicPyzo9dTyDcgHN0poukgAfEVtG1r1G9WiwHx8ipTXxZ9E+YVAMOozTjbWKPTuk4deAG9NpAGKZKR1oxvw8klxPAV+S3RyR9DRbcrYUQh1vyLojdaoGkvCylo/s8v4tS/EzNCaG/JaYYJCXphHvtd5E0k4q03EtQykGL5zTeq/vVWxPFQM/d/ro46U+Lw8UZvtGtpwXc9YnJez0j+SwNJ8kwRVwvtomDDW8lC7optjCeNj3BWV7jLV7drfJu5QO/5ypLyGNlbxBrRV5EraLhWAmcGC7hx8SdYl4cp4YTEm5QyYUOThavELlv3hBjc/9Kdi7PyeIYcaNYNtiNpBVjKIePlJ0fLeazW3KNmIYPZcB3WpqDoyfQLOAf0frn2BJkgJ2cabZ5KHNgodp8J1o/lGwMcLNITnZtvLljWCEj/k0xp5AtFnB+FTKZr0WbTKfku8QYtsiIP1+/FMiFdSInYpFo4/BaYjduEtntHOMfxdCGkLok+HDk3A6RMfaInBheHXxsxn5btPHvkBzDXBnxfTjmFLL5Af9UThypteKfok2AkoWXep1UyYcTgD8LyoLT5WzjPSv5JfF98SCxEqCfXSJjrBKvElmjrWmOZBv/EskxzJYR36Uxp5DNDzg7yt3RdLparAk1DuiOl4427BqCnwX47xBt0cgnZOmghG+90/czkn8Tb3DaNDt20mgM18nIPN+NOYVsfsA5suyEj0Vb+F7Jpb64XLpgu5R/B+SBe6zvzNNBpM0jstmavpW82PP9JrF/6elDVeJBX5+EjOjIkeWC/MbP++1JA9quEGuTeqzg8gHD9hWZ/3KaDKSwSsJSB32S9u5xOq+WXJfU33H0aeKhiYGTHESWgNMBN3qj2ElFIB+TUw+jEkF7Yhuu8pCIX5qJF4phkgkVKHn1THT6uV0y+dvgfoxy0oS9oohTEFkDTict4lynN9LFEqceEgmYnQybVMgvpOMN7I43OeSUU9egdhYDArrK6+fCpM78yzlZvKBARQNOh4+KbyIkYNfPsUpKaZMYlWIPqYdKuUz8TPwicahkwN0dzIXpgg9xQaL4SOVfrjFFHpnoba0pbt3VY6Syi4Tyyu4uXelks+NHjq8P+JlqeeJ7rynKKB+SDxftieIi0eZULRlcKt7WJe37w8V+uXiNSPoqha1yoM+fRD6uC1KNjXd/YmhWOSWRQ8U6KWnTEDLGdOclDW3AphTnM6Tny5vfNsmjxRAIDn6vh4yJrlYlflyufGQuH35aA97HNg4vlVPFX8SpouE1CeazRvKRZgiUtDffxQE7l6fZJ0heIG4QjxJDIJ10iu0ip6NssJtIFzYYJUd6nFgl+pglhev7g+oXi3Zjm/+BEr4Xd4r+bjIf23F/SMHknzCDyqNF+9GF/VfxKdHAIjtEdy4zzBgo3YByKnwwtvVFSmHep/lOTn26ZPyfdHQlxWVJIxvIL1lkCEul9H0Jio/HpcDvRt+Q1NcndnyWi/5OYSfaOCsl8xFdvKiK2Snnu0ZPfkF1fJinvzlw5aTx0fFh154jxtAiI76xjxJr3yu20eqVnbJRDO1yXjCkkLFiCJywejH2NKyTfabI4hvFnoBTzVihD+L2e74qjMdH7He4WjNicrN6cWbPq+/tYiyHV3L4VnXGJvq/xss894VqsUscn7llvAEpiNcMaWJa3LVi1gfV025xYsV67IWOSCdcRORGLulKgSdim1jpD5k2P0tdvJr6PXhGrRY/F/3LL+/kOdIj8jbO2O5c+fMLdF7Gdn3qfrBG50eK/xrp00mVOTgXe6mXS5ldFW5FBIoIFBEoIlBEoIhAtwj8B7kYiuSPD/PFAAAAAElFTkSuQmCC\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, for integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 51px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25.5px; text-align: left; transform-origin: 384px 25.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"166.5\" height=\"51\" style=\"width: 166.5px; height: 51px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe then define \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"19\" style=\"width: 44px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the sum of value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"46\" style=\"width: 129.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFinally, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ewe are asked to evaluate the integral of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, over the real range \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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width=\"204\" height=\"48\" style=\"width: 204px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"20\" style=\"width: 50px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 459.578125px 20px; transform-origin: 459.578125px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e \u0026gt;\u0026gt; a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e a = 7.05797686912156\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85.5\" height=\"18\" style=\"width: 85.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere are a number of ways to do \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003enumerical Integration\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = A(n,x1,x2) \r\n y = x;\r\nend","test_suite":"%%\r\n[n,x1,x2] = deal(1:10,pi,2*pi);\r\na_correct = [3.065357 5.25927 7.057977 8.618935 10.016842 11.294017 12.477158 13.584381 14.628646 15.619599];\r\nassert(all(abs(arrayfun(@(i) A(i,x1,x2),n)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(12,exp(1),exp(1.5));\r\na_correct = 9.752678;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(15,-2,10);\r\na_correct = 50.909769;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(25,-10*pi,0);\r\na_correct = -267.631308;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1000,0,1000);\r\na_correct = 61793.524569;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(10000,5,1234);\r\na_correct = 244011.112390;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(123456,10000,12345);\r\na_correct = 1644471.557504;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1:1000,-pi,20*exp(1));\r\na = arrayfun(@(i) A(i,x1,x2),n);\r\ns = round([sum(a) sum(diff(a,1)) sum(diff(a,2)) sum(diff(a,3))]);\r\ns_correct = [2087798 3114 -35 7];\r\nassert(isequal(s,s_correct))\r\n%%\r\n[n,x1,x2] = deal(randi(15),rand(),100*rand());\r\nt = 'sin(atan(';\r\na_correct = 0;\r\nfor i = 1:n\r\n a_correct = a_correct + integral(str2num(['@(x)' repmat('sin(atan(',1,i) 'x' repmat('))',1,i)]),x1,x2);\r\nend\r\na_correct = round(a_correct,6);\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\nfiletext = fileread('A.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-23T09:34:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-16T08:49:13.000Z","updated_at":"2023-04-23T09:34:40.000Z","published_at":"2023-04-16T17:57:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA trigonometric function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x) = \\\\sin(\\\\arctan(x))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in radians\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eApplying \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e recursively we define another function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)=\\\\underbrace{\\\\text{T}(\\\\text{T}(\\\\text{T}(...\\\\text{T}(x))))}\\\\\\\\_{\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\text{n times}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe then define \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the sum of value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n) = \\\\sum_{k=1}^{n} \\\\text{R}(x,k) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinally, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewe are asked to evaluate the integral of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, over the real range \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[x_1,x_2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=\\\\text{A}(n,x_1,x_2) = \\\\int^{x_2}_{x_1} \\\\text{S}(x,n)\\\\ \\\\mathrm{d}x}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1=\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2=2\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\\n a = 7.05797686912156]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=7.057977\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThere are a number of ways to do \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumerical Integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in Matlab. Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44694,"title":"Monte Carlo integration: area of a polygon","description":"The area of a polygon (or any plane shape) can be evaluated by \u003chttps://www.mathworks.com/matlabcentral/cody/problems/179 Monte Carlo integration\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle. \r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\u003e\u003e\r\n\r\n^\r\n\r\n*Steps:*\r\n\r\n# Define a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon. \r\n# By a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. _Other schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon)._\r\n# Determine \u003chttps://www.mathworks.com/matlabcentral/cody/problems/198 whether the sampled point is inside or outside the polygon\u003e. _Due to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null._ \r\n# Repeat steps 2–3 |N| times. \r\n# Based upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon. \r\n\r\nInputs to your function will be |N|, the number of points to sample, and |polygonX| \u0026 |polygonY|, which together constitute \u003chttps://www.mathworks.com/matlabcentral/cody/problems/194 an ordered list of polygon vertices\u003e. |N| will always be a positive integer. |polygonX| \u0026 |polygonY| will always describe a single, continuous outline; however, the polygon may be self-intersecting. \r\n\r\nFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\u003e\u003e\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\u003e\u003e\r\n\r\n^\r\n\r\nEXAMPLE\r\n\r\n % Input\r\n N = 1000\r\n polygonX = [1 0 -1 0]\r\n polygonY = [0 1 0 -1]\r\n % Output\r\n A = 2.036\r\n\r\nExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of |N| is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). \r\nOf course, if the code were run again then a slightly different value of |A| would probably be returned, such as |A|=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique. ","description_html":"\u003cp\u003eThe area of a polygon (or any plane shape) can be evaluated by \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/179\"\u003eMonte Carlo integration\u003c/a\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle.\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003e\u003cb\u003eSteps:\u003c/b\u003e\u003c/p\u003e\u003col\u003e\u003cli\u003eDefine a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/li\u003e\u003cli\u003eBy a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. \u003ci\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/i\u003e\u003c/li\u003e\u003cli\u003eDetermine \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/198\"\u003ewhether the sampled point is inside or outside the polygon\u003c/a\u003e. \u003ci\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/i\u003e\u003c/li\u003e\u003cli\u003eRepeat steps 2–3 \u003ctt\u003eN\u003c/tt\u003e times.\u003c/li\u003e\u003cli\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eInputs to your function will be \u003ctt\u003eN\u003c/tt\u003e, the number of points to sample, and \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e, which together constitute \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/194\"\u003ean ordered list of polygon vertices\u003c/a\u003e. \u003ctt\u003eN\u003c/tt\u003e will always be a positive integer. \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e will always describe a single, continuous outline; however, the polygon may be self-intersecting.\u003c/p\u003e\u003cp\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\"\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003eEXAMPLE\u003c/p\u003e\u003cpre\u003e % Input\r\n N = 1000\r\n polygonX = [1 0 -1 0]\r\n polygonY = [0 1 0 -1]\r\n % Output\r\n A = 2.036\u003c/pre\u003e\u003cp\u003eExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of \u003ctt\u003eN\u003c/tt\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). \r\nOf course, if the code were run again then a slightly different value of \u003ctt\u003eA\u003c/tt\u003e would probably be returned, such as \u003ctt\u003eA\u003c/tt\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/p\u003e","function_template":"function A = monteCarloArea(N, polygonX, polygonY)\r\n % Fun starts here\r\nend\r\n\r\n\r\n% Note: the Test Suite has been designed to account for variability in outputs. \r\n% Nevertheless, it is possible that on rare occasions a valid submission \r\n% might fail the Test Suite in one instance. \r\n% If your submission has narrowly failed only one of the test cases, \r\n% then please try resubmitting it, in case it was just due to 'bad luck'. ","test_suite":"%% No silly stuff\r\n% This Test Suite can be updated if inappropriate 'hacks' are discovered \r\n% in any submitted solutions, so your submission's status may therefore change over time. \r\n\r\n% BEGIN EDIT (2019-06-29). \r\n% Ensure only builtin functions will be called. \r\n! rm -v fileread.m\r\n! rm -v assert.m\r\n% END OF EDIT (2019-06-29). \r\n\r\nassessFunctionAbsence({'regexp', 'regexpi', 'str2num'}, 'FileName','monteCarloArea.m')\r\n\r\nRE = regexp(fileread('monteCarloArea.m'), '\\w+', 'match');\r\ntabooWords = {'ans', 'area', 'polyarea'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not do that in your code!' char([10 13]) ...\r\n 'Found: ' strjoin(RE(testResult)) '.' char([10 13]) ...\r\n 'Banned word.' char([10 13])];\r\nassert(~any( testResult ), msg)\r\n\r\n\r\n%% Unit square, in first quadrant\r\nNvec = 1 : 7 : 200;\r\npolygonX = [0 1 1 0];\r\npolygonY = [0 0 1 1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 1;\r\nassert( all(areaVec==area_correct) )\r\n\r\n%% 3×3 square, offset from origin, in all four quadrants\r\nNvec = 1 : 19 : 500;\r\npolygonX = [ 1 1 -2 -2];\r\npolygonY = [-1 2 2 -1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 9;\r\nassert( all(areaVec==area_correct) )\r\n\r\n\r\n%% Diamond, centred on origin, in all four quadrants: small N (1)\r\nN = 1;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_valid = [0 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants: small N (2)\r\nN = 2;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_valid = [0 2 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants: small N (3)\r\nN = 4;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_valid = [0:4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants: moderate N (1)\r\nN = 100;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants: moderate N (2)\r\nN = 1000;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants: moderate N (3)\r\nN = 10000;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants: large N\r\nN = 100000;\r\npolygonX = [1 0 -1 0];\r\npolygonY = [0 1 0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 7 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.0016 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.016 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants: moderate N (1)\r\nN = 100;\r\npolygonX = [ 1 -1 1 -1];\r\npolygonY = [-1 1 1 -1];\r\narea_exact = 2;\r\n\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants: moderate N (2)\r\nN = 10000;\r\nfor j = 1 : 10,\r\n rVec = 100 * rand(2);\r\n polygonX = [ 1 -1 1 -1] * rVec(1,1) + rVec(1,2);\r\n polygonY = [-1 1 1 -1] * rVec(2,1) + rVec(2,2);\r\n area_exact = 2 * rVec(1,1) * rVec(2,1);\r\n\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 12-cornered polygon of unit 'circumradius' centred on origin: moderate N\r\nN = 1000;\r\npoints = 12;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\npolygonX = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\npolygonY = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\narea_exact = polyarea(polygonX, polygonY);\r\n\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% P-cornered polygon of arbitrary 'circumradius', with centre offset from the origin: moderate N\r\nN = 1000;\r\nfor j = 1 : 10,\r\n points = randi([5 100]);\r\n centre = randi([2 100], [1 2]);\r\n circumradius = randi([2 100]);\r\n r = rand();\r\n polygonX = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n polygonY = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n area_exact = polyarea(polygonX, polygonY);\r\n\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 5-pointed star of unit 'circumradius' centred on origin: moderate N\r\nN = 1000;\r\npoints = 5;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\nx = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\ny = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\npolygonX = x([1:2:end, 2:2:end]);\r\npolygonY = y([1:2:end, 2:2:end]);\r\narea_exact = sqrt(650 - 290* sqrt(5))/4 * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n% http://mathworld.wolfram.com/Pentagram.html\r\n\r\nfor j = 1 : 3,\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% 5-pointed star of arbitrary 'circumradius', with centre offset from the origin: moderate N\r\nN = 1000;\r\npoints = 5;\r\nfor j = 1 : 10,\r\n centre = randi([2 100], [1 2]);\r\n circumradius = randi([2 100]);\r\n r = rand();\r\n x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n polygonX = x([1:2:end, 2:2:end]);\r\n polygonY = y([1:2:end, 2:2:end]);\r\n area_exact = sqrt(650 - 290* sqrt(5))/4 * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n % http://mathworld.wolfram.com/Pentagram.html\r\n\r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% P-pointed star of arbitrary 'circumradius', with centre offset from the origin: moderate N\r\nN = 1000;\r\nfor j = 1 : 20,\r\n points = 3 * randi([3 10]) - 1;\r\n centre = randi([2 100], [1 2]);\r\n circumradius = randi([2 30]);\r\n r = rand();\r\n x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n polygonX = x([1:3:end, 2:3:end, 3:3:end]);\r\n polygonY = y([1:3:end, 2:3:end, 3:3:end]);\r\n \r\n area_polyarea = polyarea(polygonX, polygonY); % Incorrect value\r\n warning('off', 'MATLAB:polyshape:repairedBySimplify')\r\n area_polyshapeArea1 = area( polyshape(polygonX, polygonY) ); % Incorrect value\r\n area_polyshapeArea2 = area( polyshape(polygonX, polygonY, 'Simplify',false) ); % Incorrect value\r\n \r\n % REFERENCE: http://web.sonoma.edu/users/w/wilsonst/papers/stars/a-p/default.html\r\n % Here: a {points/3} star\r\n k = 3;\r\n sideLength = circumradius * sind(180/points) * secd(180*(k-1)/points);\r\n apothem = circumradius * cosd(180*k/points);\r\n area_exact = points * sideLength * apothem; % Correct value\r\n fprintf('Area estimates from different methods: \\r\\npolyarea = %4.1f; polyshape.area = %4.1f or %4.1f; geometrical analysis = %4.1f\\r\\n', ...\r\n area_polyarea, area_polyshapeArea1, area_polyshapeArea2, area_exact);\r\n \r\n areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2019-06-29T13:06:05.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2018-07-02T02:19:05.000Z","updated_at":"2025-09-14T14:22:43.000Z","published_at":"2018-07-02T08:55:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe area of a polygon (or any plane shape) can be evaluated by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/179\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMonte Carlo integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSteps:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefine a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/198\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ewhether the sampled point is inside or outside the polygon\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat steps 2–3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e times.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs to your function will be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of points to sample, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which together constitute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/194\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ean ordered list of polygon vertices\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always be a positive integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always describe a single, continuous outline; however, the polygon may be self-intersecting.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026amp; middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % Input\\n N = 1000\\n polygonX = [1 0 -1 0]\\n polygonY = [0 1 0 -1]\\n % Output\\n A = 2.036]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). Of course, if the code were run again then a slightly different value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e would probably be returned, such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" 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\"},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"}]}"},{"id":60749,"title":"Compute the dispersion coefficient","description":"A contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\r\nG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \r\n\r\nwhere is the width of the stream, is the transverse mixing coefficient, and is the deviation of the velocity profile from the cross-sectional average velocity\r\n\r\nWrite a function that takes a (normalized) velocity profile specified at several points and computes the quantity \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 375px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 187.5px; transform-origin: 407px 187.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"240\" height=\"44\" alt=\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 240px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eh\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the width of the stream, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eD\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the transverse mixing coefficient, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"64\" height=\"19\" alt=\"u' = u - bar(u)\" style=\"width: 64px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"103\" height=\"44\" alt=\"ubar = (1/h) integral(u(y),0\u003c=y\u003c=h)\" style=\"width: 103px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function that takes a (normalized) velocity profile \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAkCAYAAADVeVmEAAAAAXNSR0IArs4c6QAABRhJREFUaEPtmXnIplMYxn9D9j0kIRTZsguRpUSWULLvk33ftxCy7/vOH8hOzVgKYw8hZA2RNSRKkizZzm+6Tz0ezzrvMmrmqbf55v3Oc59znfu6r/s655vADPZMmMHwMhPwCDM+F7AR8Dzw6xDmWQpYAngF+LtrvHFleFHgNOAG4P2ui2sZNwuwOzAbcEeK/0eXuOMAvFhayJnAVUMEm7G5/l2BObuCHjVgaXwh8DJwdx/qdclWjHGOc4FHgKfb3hs1YHd/U+A44Oe2xQzw+xViY48GPmuKM0rAiydRuRm4KIRqADytr4rjGGBB4Czgz7o3Rgl4P2AT4LCU4Z9alzz4gNWA64EDgffGDXgB4BbgSeDGwbF0ijAfcC3wJnB5nV6MKsNrAw+GgipY43pOAdYC9k8U/7Fq0lEBPgjYO/rk5+NCC2wHnAPsnDb7g2EDnh2QRj7W6O/x86zA2cDyTTs9ok2QWQ8D+wBTugIWyMrAsullA6wP3Bp9tBhDUbJOnwX2SGLxdfxybuDKUEqV85cWcCsBawJrpF66DrAisFeyoU8V3rPXnhesUQTvralR25O/uwy4vQ/ghdJCTwqp/wbYNn1eLwTIorQjcF302eyPF07ZvTPR640E+vSmFhHx5gXmSBnZMNzY0vHvicBvMWZ+4Kbk1HYBHo0N+aEC0HJpw+5JGzg5WPafIU01rAC4q4/FBN8X3l43ZWRSUmB77cElJc6AX6ybtCbjruXI1EuvAN4KcB8WxurHdVTayLpW1zp3HeAs8VLr/FKmrNEz4ruq7LdO2kDxVYD7Ey2l+Z7BlOJwhdD4tp2qp3XuOsC5FlYHtk9S/1AhurWtL16vJvt9KV1c+DzANcke7hugTi6IobQ3w/cBr9YAzuu2jk1UZ0pvDjxRQa1s4S6NSO50cVF+3Ve0youypXmMLIuh2T8ktKXOl2fAF1ewY+o8VRn2u1Oj/jxnFutFqpldM+9TRbtB21JuLYrZVoBaYMzjgddK6l3eLIXvhbC0XjR0ynBRgVVZaeSNgnSzv/rYbj4CVOm3K+Lapg6dRuOxSJxttywIoj5Zj2znaDp1qeInhMP7uCtggz8QxmGLaOBmXbtme3BB0tgxdRbOGLaHAyJDNSVX+bU+4ILYVOvQjycgu0Jl1iJKZpad4/C6jamitPbMPvZSIUOeehQvW4Z9d5tQabO/Q6qtb4NKGUEWn3eajHzDLqjGt8Wm6smluVdEuS9XvZqZYSI0SpVPGbD/t+X40UUdFfXqZNaQ1FYlV40N+ATYLfp1mWpuhDWuI6syCU1Z190pmj6WzMQooaZ3NoskqPC1lwBlwFo4lVeltPmbZempuXg33JCi4KN99MBtXZnh8qNb83yqyMmYPo9u664EeoMwPTq3pptJW5YXDa7RRNWOraL0TtEWXKDtQRp/F6vV7Vyd+uDWQTeZ8GUDEkvBDMuUPlnOvfyLqOW266GNQySPKKy1E6X7ZKHLWIXk2Biooa+9eikF09zINO1t27Wut6Ky7ZJoW43rGtV5uDipZeLlmhfmz3S4uZSenmk93uU6rgPRN/bY/tTiwqSbAvR4A2gToAguGUe8psv1HFOb+VyHjZy6aePIcM6OfylYBrAuMxBNjqKo2nue1mx4FtdPN7UgY9qGZMNXXWorjxkn4PK6iqcuj4FayE/TLYo+ve3SoA/Gf42dnoBdiNZUsTHrGn4P939NM5oOL05vwB2WONwhMwEPdz//f9H+AX/HFDSie/GkAAAAAElFTkSuQmCC\" width=\"30\" height=\"18\" alt=\"u(y)\" style=\"width: 30px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e specified at several points and computes the quantity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"215\" height=\"44\" alt=\"I = -integral(u' integral(integral(u'(y2),0\u003c=y2\u003c=y1),0\u003c=y1\u003c=y),0\u003c=y\u003c=h)\" style=\"width: 215px; height: 44px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = computeK(y,u)\r\n I = -integral(u'*integral(integral(u',0,y1),0,y),0,h);\r\nend","test_suite":"%%\r\nny = 1000;\r\ny = linspace(0,1,ny);\r\nu = y.*(1-y);\r\nI = computeK(y,u);\r\nI_correct = 1/7560;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = 2*y;\r\nu(y\u003e1/2) = 2*(1-y(y\u003e1/2));\r\nI = computeK(y,u);\r\nI_correct = 1/480;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6);\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\ny = linspace(0,1,ny);\r\nu = sin(pi*y);\r\nI = computeK(y,u);\r\nI_correct = 5/(6*pi^2)-8/pi^4;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 2.5;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.00788915;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 2.5; \r\nb = 3;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01168232;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)\r\n\r\n%%\r\nny = 10000;\r\na = 3.2; \r\nb = 3.2;\r\ny = linspace(0,1,ny);\r\nu = gamma(a+b)*y.^(a-1).*(1-y).^(b-1)/(gamma(a)*gamma(b));\r\nI = computeK(y,u);\r\nI_correct = 0.01192484;\r\nassert(abs(I-I_correct)/I_correct \u003c 1e-6)","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2024-10-16T01:19:16.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-10-16T01:18:30.000Z","updated_at":"2024-10-27T15:58:26.000Z","published_at":"2024-10-16T01:19:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA contaminant dumped or spilled into a river will move downstream with the flow, but it will also spread in the flow direction because of several mechanisms. One of these mechanisms is shear dispersion: the spreading results because the velocity varies across the cross section, and parcels of the contaminant sample different velocities as eddies transport them across the cross section.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eG.I. Taylor showed that the concentration averaged over the cross section evolves according to an advection-diffusion equation, and the dispersion coefficient can be computed with \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K = -(1/hD) integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK = -\\\\frac{1}{hD}\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"h\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the width of the stream, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"D\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eD\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the transverse mixing coefficient, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u' = u - bar(u)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu^\\\\prime = u-{\\\\bar u}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the deviation of the velocity profile from the cross-sectional average velocity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"ubar = (1/h) integral(u(y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e{\\\\bar u} = \\\\frac{1}{h} \\\\int_0^h u(y) dy\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that takes a (normalized) velocity profile \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"u(y)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eu(y)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e specified at several points and computes the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"I = -integral(u' integral(integral(u'(y2),0\u0026lt;=y2\u0026lt;=y1),0\u0026lt;=y1\u0026lt;=y),0\u0026lt;=y\u0026lt;=h)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eI = -\\\\int_0^h u^\\\\prime \\\\int_0^y \\\\int_0^{y_1} u^\\\\prime(y_2) dy_2 dy_1 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