# Math 121 - Exam 5 Study Guide

1. A graph of a function is shown. Use rectangles to approximate the area under the curve. Look at problem 21 in the chapter 5 review.
2. Find the derivative and state a corresponding integration formula. Look at problems 5.2.5-8.
3. Express the Riemann Sum as a definite integral. Do not evaluate. Look at problems 5.5.5-8.
4. Evaluate the summation. Two parts. Look at problems 5.4.11-16.
5. Use the areas shown in the figure to find the definite integrals. Six parts. Look at problem 5.5.17-22.
6. Use part 2 of the fundamental theorem of calculus to evaluate the derivative. Look at problems 5.6.43-46.
7. Find a polynomial function with integer coefficients having the indicated extrema and y-intercept. Use the fact that extrema of a polynomial occur when f'(x)=0 to find the derivative function and then integrate to find the original function f. After obtaining integer coefficients (multiply by LCD), use the y-intercept as an initial value.
8. A particle moves along an s-axis. Use the given information to find the position function of the particle. Look at problems 5.7.5-8.
9. Evaluate the indefinite integrals without using substitution. Five parts. Look at problems 5.2.9-30.
10. Evaluate the definite integrals without using substitution. Three parts. Look at problems 5.6.7-19.
11. Use a u-substitution to rewrite the integrals. Do not evaluate the integrals, only rewrite them in terms of u. Look at problems 5.8.1-2.
12. Use method 1 (dropping the limits) of substitution to evaluate the definite integral. Look at problems 5.8.3-12.
13. Use method 2 (changing the limits) of substitution to evaluate the definite integral. Look at problems 5.8.3-12.
14. Evaluate the definite integral using either method of substitution. Look at problems 5.8.21-34.

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 8 4 4 8 12 4 5 5 20 12 6 4 4 4 100