Math 221: Chapter 15 Study Guide

  1. Evaluate the iterated integrals. Two parts. Look at problems 15.1.1-12 and 15.2.1-10
  2. Express the integral as an equivalent integral with the order of integration reversed. Do not evaluate. Look at problems 15.2.41-46
  3. Evaluate a double integral over the region described. Look at problems 15.2.31-38.
  4. Evaluate the iterated integral by converting to polar coordinates. Look at problems 15.3.23-30.
  5. Find the surface area. Look at problems 15.4.35-46
  6. Find the equation of the tangent plane to the parametric surface at the stated point. Look at problems 15.4.29-34
  7. Sketch the solid whose volume is given by the integral and then find the volume. Look at problems 15.5.23-24
  8. Find the centroid of the region enclosed. Look at problems 15.6.5-10
  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 15.6.37-40
  10. Use cylindrical coordinates to find the volume of a solid. Look at problems 15.7.5-8, 13-16, 31-36
  11. Use spherical coordinates to find the mass of a solid. Look at problems 15.7.23-24, 31-36
  12. Solve for x and y in terms of u and v and then find the Jacobian. Look at problems 15.8.5-8
  13. Evaluate the integral by making an appropriate change of variables. Look at problems 15.8.31-34
  14. 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.
  15. 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:

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