## Math 121 - Chapter 7 Study Guide

- Evaluate the integral. Four parts. Look at problems 7.2.13-30.
- Evaluate the integrals by making appropriate substitutions. Three parts. Look at problems 7.3.5-36.
- Express the Riemann Sum as a definite integral. Do not evaluate. Look at problems 7.5.33-34.
- Write the expression in sigma notation, but do not evaluate. Two parts. Look at problems 7.4.3-12.
- Express the sum in closed form. Look at problems 7.4.23-28.
- Use the areas shown in the figure to find the definite integrals. Look at problem 7.5.21.
- Identify the true identities. Twenty-six parts. Look at problems 7.4.49-50, but also any properties of summation,
integration, differentiation, and limits. These are things like "the integral of a sum is the sum of the integrals".
- Sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate
formula from geometry, where needed. Look at problems 7.5.17-20.
- Evaluate the integrals using the first fundamental theorem of calculus. Three parts. Look at problems 7.6.9-24.
- Use the second fundamental theorem of calculus to find the derivative. Look at problems 7.6.45-50.
- A particle moves along an s-axis. Use the given information to find the position function of the particle. Look at
problems 7.7.7-10.
- Find the average value of the function over the given interval. Find all values guaranteed by the mean value theorem for
integrals and then draw a figure that illustrates the mean value theorem for integrals. Look at problems 7.7.49-54
- Evaluate the definite integrals using substitution. Two parts. Look at problems 7.8.23-38
- A particle moves with the given acceleration and initial velocity. Find the displacement and distance traveled by the
particle during the time period. Look at problems 7.7.15-18.

### Notes:

- Some of the problems are directly from the text.
- There is an extra-credit, take home portion of this exam worth 15 points if you're interested. It will be due on Thursday,
December 7.

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

Pts |
12 |
12 |
3 |
6 |
4 |
10 |
13 |
4 |
9 |
4 |
5 |
6 |
8 |
4 |
100 |