Example 9.  Let  .  Use the Monte Carlo method to calculate approximations to the integral  

        .  

Solution 9.

We are done!

Aside.  We can use Mathematica's subroutine NIntegrate to perform Monte Carlo integration, and we can verify that it is computing the same results as our subroutine MonteCarloIntegral4D.

(c) John H. Mathews 2005