## Math 221- Chapter 17 Study Guide

1. Evaluate the iterated integrals. Two parts. Look at problems 17.1.1-14* and 17.2.1-12*
2. Express the integral as an equivalent integral with the order of integration reversed. Look at problems 17.2.49-56*
3. Evaluate a double integral over the region described. Look at problems 17.2.13-28*
4. Evaluate the iterated integral by converting to polar coordinates. Look at problems 17.3.23-30*
5. Find the surface area. Look at problems 17.4.1-10*
6. Find the surface area for a vector valued function. Look at problems 17.4.17-22*
7. Use a triple integral to find a volume. Look at problem 17.5.13-21,30*
8. Find the centroid of the region enclosed. Look at problems 17.6.7-13*
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.
10. Use cylindrical coordinates to find the volume of a solid. Look at problems 17.7.5-9, 16-18, 22-24*
11. Use spherical coordinates to find the volume of a solid. Look at problems 17.7.10-14, 19-21, 25-27*
12. Solve for x and y in terms of u and v and then find the Jacobian. Look at problems 17.8.5-8*
13. Use the transformations given to evaluate the integral. Look at problems 17.8.13-18*
14. Evaluate the integral by making an appropriate change of variables. Look at problems 17.8.27-31*
15. Consider the region described. Identify which double integrals are written with the proper limits and order of integration to find the area of the region. Twelve integrals to choose from, choose all that are correct.

### Notes:

• *'d problems are directly from the text.
• 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
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total Pts 10 5 6 6 7 7 7 7 7 7 7 5 7 7 5 100