# Math 121 - Exam 5 Study Guide

- 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.
- Find the derivative and state a corresponding integration formula. Look
at problems 5.2.5-8.
- Express the Riemann Sum as a definite integral. Do not evaluate. Look
at problems 5.5.5-8.
- Evaluate the summation. Two parts. Look at problems 5.4.11-16.
- Use the areas shown in the figure to find the definite integrals. Six
parts. Look at problem 5.5.17-22.
- Use part 2 of the fundamental theorem of calculus to evaluate the derivative.
Look at problems 5.6.43-46.
- 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.
- 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.
- Evaluate the indefinite integrals without using substitution. Five parts. Look at problems 5.2.9-30.
- Evaluate the definite integrals without using substitution. Three parts. Look at problems 5.6.7-19.
- 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.
- Use method 1 (dropping the limits) of substitution to evaluate the definite integral. Look at problems 5.8.3-12.
- Use method 2 (changing the limits) of substitution to evaluate the definite integral. Look at problems 5.8.3-12.
- Evaluate the definite integral using either method of substitution. Look at problems 5.8.21-34.

## Point values per problem

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

Pts |
8 |
4 |
4 |
8 |
12 |
4 |
5 |
5 |
20 |
12 |
6 |
4 |
4 |
4 |
100 |