MATLAB: Numerical double integral of an expression with vector defined variables

for loopMATLABmatrixnumerical integration

Hi everyone,
I have to compute double integral for the expression G over phi and theta in the following code numerically. Does anyone have any idea how it must be done, since it is not easy to use trapz or integral2 because of the definition of the variables! 
c = 4.2;
d = 10;
r3 = linspace(c, d, 100);
theta = linspace(-pi/2, pi/2, 100); 
theta2 = linspace(-pi/2 ,pi/2, 100); 
Phi = linspace(0, 2*pi, 100);
Phi2 = linspace(0, 2*pi, 100);
G =  r3.*(sin(theta2).*cos(theta).*cos(phi2-phi) - cos(theta2).*sin(theta)) ./(r3.^2 + c.^2 - 2.*r3.*c.*(sin(theta2).*sin(theta).*cos(phi2-phi)+cos(theta2).*cos(theta))).^3/2 ;

Best Answer

Here is a start
phi = linspace(...)             % define value for phi
theta = linspace(...);          % define theta
dphi = phi(2)-phi(1);           % phi step
dtheta = theta(2)-theta(1);     % theta step
[PHI,THETA] = meshgrid(phi,theta);      % create 2D grid
G = PHI .. THETA ...            % calculate G at each point of grid
F = G(1:end-1,1:end-1) + G(1:end-1,2:end) + G(2:end,1:end-1) + G(2:end,2:end);
result = sum(F(:))/4*dphi*dtheta*
Do you know why F variable is so long?
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