# Math 121: Chapter 5,7 Exam Study Guide

- Find the area between two curves.
- Find the volume of the solid of revolution.
- Find the volume of the solid of revolution.
- Find the length of a curve.
- Find the surface area of revolution.
- Find the work for a spring problem.
- Find the center of mass for the region.
- Find the fluid force on a vertically submerged surface.
- Integrate. This is a little bit of everything from chapters 4 and 5. You will need to know how to do u-substitutions as well as use a geometry formula to evaluate an integral. Seven parts.
- Find the derivative. This is a little bit of everything from chapter 2 and 5. You will need to know all of the derivative rules including implicit differentiation. You may save yourself a lot of work by using properties of logarithms. Five parts.
- Use the second fundamental theorem of calculus to find the derivative of an integral.
- Find the limit. In particular, pay careful attention to the three trig limits you are to have memorized. Two parts.

## Notes

- Most of the problems are similar to those in the textbook.
- In questions 1-8, you are to show your work as far as coming up with the definite integral and then use the numeric integration feature on your calculator to evaluate the definite integral.
- There are 113 points possible, but the exam is only worth 100 points in the gradebook, so here is a chance for you to recoup some of the points missed on other tests.
- There is a take home exam worth 36 points that is due when you come in to take the final exam.
- This is a final exam and while mostly over chapters 5 and 7, there are a few questions over previous chapters. You have 2 hours to take the exam, beginning at 12:00 noon on Monday, December 13.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
TH1 |
TH2 |
Total |

Pts |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
21 |
15 |
3 |
6 |
12 |
24 |
113 |