## Math 221- Chapter 16 Study Guide

1. Evaluate the iterated integrals. Two parts. Look at problems 16.1.1-12 and 16.2.1-10
2. Express the integral as an equivalent integral with the order of integration reversed. Look at problems 16.2.41-46
3. Evaluate a double integral over the region described. Look at problems 16.2.13-22
4. Evaluate the iterated integral by converting to polar coordinates. Look at problems 16.3.23-30
5. Find the surface area. Look at problems 16.4.35-46
6. Find the equation of the tangent plane to the parametric surface at the stated point. Look at problems 16.4.29-34
7. Sketch the solid whose volume is given by the integral and then find the volume. Look at problems 16.5.23-24
8. Find the centroid of the region enclosed. Look at problems 16.6.5-10
9. 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
10. Use cylindrical coordinates to find the volume of a solid. Look at problems 16.7.5-8, 13-16, 31-36
11. Use spherical coordinates to find the mass of a solid. Look at problems 16.7.23-24, 31-36
12. Solve for x and y in terms of u and v and then find the Jacobian. Look at problems 16.8.5-8
13. 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