**Example 7.** Use
Monte Carlo simulation to approximate the area of the region defined
by the constraints

**Solution 7.**

Set up the constraints for the region.

Set up the rectangular box enclosing the area.

Use Monte Carlo simulation and explore what happens with points.

We are done.

**Aside.** The analytic
value of the area can be found by splitting it up into three
parts.

The curved portion at the top from and the curved portion at the bottom from are given by the following formulas.

The curved portion at the left from and the curved portion at the right from are given by the following formulas.

(c) John H. Mathews 2005