Evaluate double integral using trapezoidal rule

I have an assignment to evaluate a double integral using trapezoidal rule. The first part was to evaluate a double integral using trapezoidal rule with limits 0 <= x <= 2, 0 <= y <= 1

I have a working script for that:

N = 100;
xh= 1.25;
x = linspace(0,2,N);
y = linspace(0,1,0.5*N);
dx = diff(x(1:2));
dy = diff(y(1:2));
[x,y] = meshgrid(x,y);
funk = exp(-10.*((x-xh).^2+y.^2)).*cos(y.*(x-xh));
funk(2:end-1,:) = funk(2:end-1,:)*2;
funk(:,2:end-1) = funk(:,2:end-1)*2;
out = sum(funk(:))*dx*dy/4;

disp(out)

Now for the second part the limits are 0 <= x <= 2, 0 <= y <= ((pi*x)/2)

How do I get y (line 4 in code) to take corresponding x values from the x-matrix to create the y-matrix? If I get that to work I shouldn't have to change anything else in the code right, or am I missing something?

Answer 1

[Sean de Wolski]

How about instead of re-linspacing:

y = pi*x/2

[Mark Johnson]

How do you mean? Maybe I'm misinterpreting you but won't that give me just one value for y. From my understanding I need a matrix, the same size as x, for y.

[Sean de Wolski]

x is a vector (output from linspace) so x multiplied my scalars will also be a vector.

Run it!