I want to use this method to evaluate a triple integral that is otherwise impossible (not elementary). The region is the unit sphere. The Monte Carlo method sounds simple, but if I were to use MATLAB to do this, how would I pick my random sample points so that they are INSIDE the region? Are there any efficient methods for doing this, besides chosing points randomly from the unit cube and checking them all to see that they are inside the sphere? This selection process sounds inefficient, especially for regions other than spheres. Does anyone have any tips?