Cody

Problem 47043. Find the Arc Length of the Curve Defined by the Parametric Functions

Solution 3349863

Submitted on 23 Oct 2020 by William
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Test Suite

Test Status Code Input and Output
1   Pass
interval=[0,2*pi]; a=3; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 16; assert(abs(arcLength(x,y,interval)-S)<1e-3)

2   Pass
interval=[0,2*pi]; a=5; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 32; assert(abs(arcLength(x,y,interval)-S)<1e-3)

3   Pass
interval=[0,2*pi]; a=7; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 48; assert(abs(arcLength(x,y,interval)-S)<1e-3)

4   Pass
interval=[0,6*pi]; a=7; b=3; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 96; assert(abs(arcLength(x,y,interval)-S)<1e-3)

5   Pass
interval=[0,10*pi]; a=11; b=5; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 240; assert(abs(arcLength(x,y,interval)-S)<1e-3)

6   Pass
interval=[0,2*pi]; x=@(t)5*(t-sin(t)); y=@(t)5*(1-cos(t)); S=40; assert(abs(arcLength(x,y,interval)-S)<1e-3)

7   Pass
interval=[0,100*pi]; a=pi; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 856.288; assert(abs(arcLength(x,y,interval)-S)<1e-3)