# Study Guide - Chapter 14

## Math 221

- Evaluate the multiple integral. Change the coordinate system when convenient. In each case,
sketch the region of integration. Three parts. Look at problems 3 - 12 in the review*
- Consider the region described. Write the limits for the double integral for both orders and
compute the area of the region. Look at problems 17 - 24 in the review*.
- Use a multiple integral and a convenient coordinate system to find the volume of the solid.
Two parts. Look at problems 25 - 30 in the review*.
- Find the center of mass of the solid of uniform density bounded by the given equations. Look
at problems 37 - 40 in the review*.
- Perform a change of variables to evaluate the integral. Look at problems 9 - 14 and 23 in
section 14.8*.

All problems are directly from the textbook with the exception that problem 1 also asks for a
sketch of the region of integration.

The in-class portion of the test is 60 points.

The take home portion of the tests is 40 points.

- 14.2.62
- 14.3.30
- 14.4.30
- 14.5.36
- 14.6.18
- 14.7.38
- 14.8.22
- 14.8.27-28