How do you apply simpsons rule to double and triple integrals?

http://en.wikipedia.org/wiki/Simpson%27s鈥?/a>How do you apply simpsons rule to double and triple integrals?
The Wikipedia article on Simpson's Rule says nothing about multiple integrals.





Unfortunately Simpson's rule can't be applied directly to multiple integrals. What you need to do is derive interpolant surfaces or hypersurfaces for double or triple integrals, respectively. For a double integral you end up evaluating the function on a grid of nine points instead of the three points you use in the single integral case. For a triple integral you use a 3-D lattice of 27 points. Needless to say, it gets pretty complicated.





An easier approach is some sort of Monte Carlo integration, in which you randomly sample the function many times, take the average of all the function samples, and multiply by the area of integration. The drawback here is that the error is inversely proportional to the square root of the number of samples, so 4 times as many samples only halves your expected error. If you have plenty of time and your accuracy requirements aren't great, this is probably the approach you should try.How do you apply simpsons rule to double and triple integrals?
dont know