Why does MATLAB grader refuses to get my answer with the double integral evaluation problem?

Hello,

I am new to MATLAB, and my teacher gave us a few questions.

I am using the MATLAB grader to check whether or not my answer is correct.

I got the following question:

"Use the meshgrid command to evaluate the double integral that has limits of 0 to 2*pi each, with the integrand of ((sin(x)^2) * (cos(y)^2)dxdy): by approximating the volumes of 0.01x0.01 squared boxes that lie below the graph of the function".

I tried and wrote the following code:

x = linspace(0, 2*pi, 1000);
y = linspace(0, 2*pi, 1000);
[X, Y] = meshgrid(x, y);
Z = (sin(X).^2).*(cos(Y).^2);
L = sum(sum(Z))*(2*pi/1000)^2;

I get the result: 9.8696 which is 2 times the result I should have got. Even after dividing by 2 I get the following error in MATLAB grader:

"The value of L is incorrect".

I don't seem to understand why the grader doesn't work.

I hope that I have made myself clear.

If you know how to resolve this, your help would be much appreciated.

Answer 1

[Alan Stevens]

As follows

Oops! I did the sum incorrectly! Should have been like this:

% box side length
delta = 0.01;

% mid box points
x = delta/2:delta:(2*pi-delta/2);
y = delta/2:delta:(2*pi-delta/2);

% values of Z summed for each column 
Z = 0;
for i = 1:numel(x)
Z = sum((sin(x(i))^2)*(cos(y).^2))+Z;
end

L = Z*delta^2;
disp(L)

    9.8596

to get same as Omer got!

[Torsten]

integral(@(x)sin(x).^2,0,2*pi)*integral(@(x)cos(x).^2,0,2*pi)

ans = 9.8696

So the result the OP got looks fine to me.