# Math 121: Chapter 4 Exam Study Guide

1. Find the indefinite integral; show work. Five parts.
2. 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.
3. 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.
4. 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.
5. Given the values of two definite integrals, use them to find other definite integrals.
6. A region is shown. Find the area using geometric formulas. Then write the area as the sum of definite integrals.
7. Given a function F(x) = integral(f(t),t,a,x), find F(a), F'(a), and F"(a).
8. Evaluate the definite integrals. Show work and give exact answers.
9. Rewrite the integral and limits in terms of u and then evaluate the definite integral.
10. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 TH1 TH2 Total 15 6 8 9 8 6 6 12 4 6 11 9 100