How to find a double integral

I need to integrate the function wrt theta and phi. How to do it? m,n, p are constants.

f=m*p*cos(theta)^3*sin(phi)^2 - n*p*cos(phi)^2*cos(theta)^3 - m*n*cos(theta)*sin(phi)^2*sin(theta)^2 + m*n*cos(phi)*cos(theta)*sin(phi)*sin(theta)^2

Answer 1

[Star Strider]

It is best to vectorize your function using element-wise operations, then create it as a function of the two variables, then use integral2 to numerically integrate it:

m = 3;
n = 5;
p = 7;
f = @(theta,phi) m*p*cos(theta).^3.*sin(phi).^2 - n*p*cos(phi).^2.*cos(theta).^3 - m*n*cos(theta).*sin(phi).^2.*sin(theta).^2 + m*n*cos(phi).*cos(theta).*sin(phi).*sin(theta).^2;
f_int = integral2(f, 0, 2*pi, 0, 2*pi)

I created values for the constants to test the code.

Answer 2

[Hirak]

Thanks to you two....

[Star Strider]

As always, our pleasure.