I need to integrate a function (of two variables). I know I can do it by using Fubini theorem to integrate one variable functions, then using numerical methods such
I would recommend Gaussian quadrature and linear shape functions:
http://www.mathworks.com/matlabcentral/fileexchange/9230-gaussian-quadrature-for-triangles
http://www.wolframalpha.com/input/?i=gaussian+quadrature+triangle
http://www.cs.rpi.edu/~flaherje/pdf/fea6.pdf