# Math 121: Chapter 5,7 Exam Study Guide

1. Find the area between two curves.
2. Find the volume of the solid of revolution.
3. Find the volume of the solid of revolution.
4. Find the length of a curve.
5. Find the surface area of revolution.
6. Find the work for a spring problem.
7. Find the center of mass for the region.
8. Find the fluid force on a vertically submerged surface.
9. 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.
10. 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.
11. Use the second fundamental theorem of calculus to find the derivative of an integral.
12. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 TH1 TH2 Total 4 4 4 4 4 4 4 4 21 15 3 6 12 24 113