## Math 221- Chapter 16 Study Guide

- Evaluate the iterated integrals. Two parts. Look at problems 16.1.1-12 and 16.2.1-10
- Express the integral as an equivalent integral with the order of integration reversed. Look at problems 16.2.41-46
- Evaluate a double integral over the region described. Look at problems 16.2.13-22
- Evaluate the iterated integral by converting to polar coordinates. Look at problems 16.3.23-30
- Find the surface area. Look at problems 16.4.35-46
- Find the equation of the tangent plane to the parametric surface at the stated point. Look at problems 16.4.29-34
- Sketch the solid whose volume is given by the integral and then find the volume. Look at problems 16.5.23-24
- Find the centroid of the region enclosed. Look at problems 16.6.5-10
- Use the Theorem of Pappus to find the volume of the solid of revolution of the region about a line. Be sure you can find
the distance between a point and a line. Look at problems 16.6.35-39
- Use cylindrical coordinates to find the volume of a solid. Look at problems 16.7.5-8, 13-16, 31-36
- Use spherical coordinates to find the mass of a solid. Look at problems 16.7.23-24, 31-36
- Solve for
*x* and *y* in terms of *u* and *v* and then find the Jacobian. Look at problems 16.8.5-8
- Evaluate the integral by making an appropriate change of variables. Look at problems 16.8.27-31

### Notes:

- You may use notecards with the following formulas on them.
- Finding area in polar coordinates.
- Finding volume in cylindrical and spherical coordinates
- The conversion formulas between rectangular, cylindrical, and spherical coordinates
- The formulas for the moments about the x and y axes
- The formulas for the moments of inertia

- There may not be any examples on the notecards.
- Although not explicitly stated with each problem, part of what I will be grading is the sketch of the region where
appropriate.

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
Total |

Pts |
10 |
7 |
7 |
7 |
7 |
8 |
7 |
8 |
8 |
8 |
8 |
7 |
8 |
100 |