Steve, I'm quite unsure about how one would proceed with this. First of all, I guess I would have to use integral2 since I'm performing a surface integral. Second of all, it doesn't seem like MATLAB likes numerically integrating a matrix per entry. I was trying the below example as a demonstrator.
q = integral2(b,0,1,0,1)
I get a bunch of errors. I have no doubt that I can extract each entry from the matrix individually, define it as a function, and then integrate it numerically. However, there are so many operations here that it seems at first glance it wouldn't be efficient.