How can I upgrade the multi variable integration?

Hello. I'd like to integrate the multi variable equation as attached using trapezoidal integral.

So I made the code as attached abbreviated m-file and function.

However, in the original code I made, it takes too many time because I used many for-end structure.

I'm trying to reduce the calculation time, but it's too hard to me. Could you please help me or recommend any thing for that?

Many Thanks indeed, Best regard.

(I'm using MATLAB 2015a.)

Answer 1

[Kuifeng]

 %see example of matlab, use double or triple trapz, 
F = X.^2 + Y.^2;
I = trapz(y,trapz(x,F,2))