# Math 221: Chapter 15 Study Guide

- Evaluate the iterated integrals. Two parts. Look at problems 15.1.1-12
and 15.2.1-10
- Express the integral as an equivalent integral with the order of integration
reversed. Do not evaluate. Look at problems 15.2.41-46
- Evaluate a double integral over the region described. Look at problems
15.2.31-38.
- Evaluate the iterated integral by converting to polar coordinates.
Look at problems 15.3.23-30.
- Find the surface area. Look at problems 15.4.35-46
- Find the equation of the tangent plane to the parametric surface
at the stated point. Look at problems 15.4.29-34
- Sketch the solid whose volume is given by the integral and then
find the volume. Look at problems 15.5.23-24
- Find the centroid of the region enclosed. Look at problems
15.6.5-10
- 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 15.6.37-40
- Use cylindrical coordinates to find the volume of a solid.
Look at problems 15.7.5-8, 13-16, 31-36
- Use spherical coordinates to find the mass of a solid.
Look at problems 15.7.23-24, 31-36
- Solve for x and y in terms of u and v and then find
the Jacobian. Look at problems 15.8.5-8
- Evaluate the integral by making an appropriate
change of variables. Look at problems 15.8.31-34
- Find a transformation that will transform the
region in the xy-plane into the region in the uv-plane.
Look
at problems
15.8.27-30.
- Write a double integral that can be used to
find the area of the region. Write it as both
a type I
and type
II integral.
Do
not evaluate
the integral.

## Notes:

- You may place the conversion formulas between rectangular, cylindrical,
and spherical coordinates onto notecards. You may not place examples onto
the notecards.
- Although not explicitly stated with each problem, part of what I will
be grading is the sketch of the region where appropriate.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
Total |

Pts |
10 |
5 |
7 |
7 |
7 |
7 |
7 |
7 |
7 |
7 |
7 |
5 |
6 |
5 |
6 |
100 |