How to perform multivariable numerical integration?

[Topher925]

I've got a problem where I need to numerically integrate a multivariable function but I'm not sure how to do this. I'm more than familiar with how to numerically integrate a single variable function numerically but I have no clue how to do this for a multivariable function. For example let's say I have the function

P = (x² + 4xy)

and I need to integrate this numerically between some definite closed bounds of x, y, and z using the trapezoidal rule. How would one go about doing this? Would I simply perform the integration on each variable and then plug that solution into the respective variable for that function for each integral I evaluate? I have two books on numerical methods and none of them mention anything about doing this. Is it even possible?

 

[Topher925]

Nevermind, I figured it out. Just had a bit of a stupid moment.

 

[MichaelMi]

For the record: with 2 variables, see H. Engels, "Numerical Quadrature and Cubature", Academic, 1980. For many variables, use Monte Carlo integration.