**Example
8.** Let . 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