# Math 121: Chapter 4 Exam Study Guide

- Find the indefinite integral; show work. Five parts.
- Write the expression in summation notation. Example 1/2 + 2/3 + 3/4 + 4/5 + 5/6 + ... + 19/20 would be the sum from k = 1 to 19 of k/(k+1) -- but be sure to write it in symbols. Two parts.
- Given a summation formula, use it to find a finite sum (example, the sum from k=1 to 5 of whatever) and a closed form. Then use the closed form to evaluate the sum for a larger value of n and then finally find the limit of the closed form as n approaches infinity.
- You are given the closed forms for the sums of one, the sum of the integers, and the sum of the squares of the integers. Use it to find a sum for a value of n, the general closed form, and the limit as n approaches infinity of an expression.
- Given the values of two definite integrals, use them to find other definite integrals.
- A region is shown. Find the area using geometric formulas. Then write the area as the sum of definite integrals.
- Given a function F(x) = integral(f(t),t,a,x), find F(a), F'(a), and F"(a).
- Evaluate the definite integrals. Show work and give exact answers.
- Rewrite the integral and limits in terms of
*u* and then evaluate the definite integral.
- Use the second fundamental theorem of calculus to evaluate. Two parts.

## Notes

- Most of the problems are similar to those in the textbook. Some of the problems are directly from the textbook.
- A few of the problems are like examples worked in class that weren't like anything in the textbook (particularly #7).
- Don't spend too long on any one problem. If you get stuck, make a note to come back and then move on.
- There is a take home exam worth 20 points that is due the day of the in-class test.

## Points per problem

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

Pts |
15 |
6 |
8 |
9 |
8 |
6 |
6 |
12 |
4 |
6 |
11 |
9 |
100 |