# Math 221: Chapter 16 Study Guide

1. Find div F and curl F. Look at problems 16.1.13-18.
2. Find a parametrization for the given curve and use it to evaluate the line integral. Look at problems 16.2.21-24.
3. Evaluate the line integrals. Two parts. Look at problems 16.2.7-10 and 16.2.11-18.
4. Show that the integral is independent of path and find its value. Look at problems 16.3.9-14.
5. Show that F is conservative and find a potential function for it. Look at problems 16.3.1-6.
6. Use Green's theorem to evaluate the line integral. Look at problems 16.4.3-13.
7. Evaluate the surface integral over the surface represented by a vector valued function r. Look at problems 16.5.27-30.
8. Evaluate the surface integral. Look at problems 16.5.1-10.
9. Find the flux of the vector field F across the surface. Look at problems 16.6.7-12.
10. Use the Divergence Theorem to find the flux of F across the surface σ with outward orientation. Look at problems 16.7.5-15.
11. Use Stoke’s Theorem to evaluate the integral. Look at problems 16.8.7-14.

## Notes

• Most of the the problems are directly from the text.
• Show work, but you may use Derive to evaluate the integrals.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 Total 12 8 16 8 8 8 8 8 8 8 8 100