Example 8.  Let  [Graphics:Images/MonteCarloMod_gr_210.gif].  Use the Monte Carlo method to calculate approximations to the triple integral  


Solution 8.










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 MonteCarloIntegral3D.





Observe that the results are the same.

We are really done!  

Aside.  The analytic value of the integral can be found and involves the following steps.






























(c) John H. Mathews 2005