I am not able to integrate heaviside(y-f) for x= 0 to pi/2 and y = 0 to pi/2 (only syms integration "int"). After running the code, output is shown in below and i am not able to get the numerical answer. Can you give some ideas on how to proceed?

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syms x y
f = sin(x);
integ = int( int(heaviside(y-f), x, 0, pi/2),y, 0, pi/2)
integ =
int(int(heaviside(y - sin(x)), x, 0, pi/2), y, 0, pi/2)
Walter Roberson
Walter Roberson on 14 Aug 2020
For your purposes, is heaviside(0) equal to 0, or is it equal to 1, or is it equal to 1/2, or is it undefined ?

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Accepted Answer

Walter Roberson
Walter Roberson on 13 Aug 2020
Reverse the order of integration.
>> integ = int( int(heaviside(y-f), y, 0, pi/2),x, 0, pi/2)
integ =
pi^2/4 - 1

More Answers (1)

hosein Javan
hosein Javan on 13 Aug 2020
if you need numerical integration, some functions cannot be easily evaluated by symbolic. instead use "integral". in here we have a double integral. the integral calculation method is 'iterated' which means on each iteration it is integrating on one dimension and then the next. it takes a few seconds to accomplish though.
fun = @(x,y) double( y > sin(x) )
q = integral2(fun, 0, pi/2, 0, pi/2, 'Method', 'iterated', 'Reltol', 1e-8)
% answer in command window:
q =
here's your function plot. blue part is zero. yellow part equals one.
actually i need to do syms int type of integration, but as you suggested i will also look into integral2 command. Thank you very much.

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