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