Math 222

Homework #3

Instructions. This is due on February 20 at the beginning of class. It is worth 20 points. Late papers lose 3 points per day late. You must work by yourself, but feel free to consult with me. Explain what you did and why you did it: good explanations are essential! Start early, ask questions and do well.

Problems. In this assignment, you will explore a clever way of using random numbers to estimate integrals. This technique is commonly used by scientists, engineers and mathematicians.

Work exploratory exercise 2 on page 1046. Note that the problem discussed while introducing the method is much simpler than the one you are asked to work. For the last problem, 20 points is enough to illustrate the method, although you will probably get a bad estimate of the integral. Be sure to list your random points and function values, and explain how you decide whether or not the point is in the region of integration (this is not easy!).