## Math 121 - Chapter 7 Study Guide

1. Evaluate the integral. Four parts. Look at problems 7.2.13-30.
2. Evaluate the integrals by making appropriate substitutions. Three parts. Look at problems 7.3.5-36.
3. Express the Riemann Sum as a definite integral. Do not evaluate. Look at problems 7.5.33-34.
4. Write the expression in sigma notation, but do not evaluate. Two parts. Look at problems 7.4.3-12.
5. Express the sum in closed form. Look at problems 7.4.23-28.
6. Use the areas shown in the figure to find the definite integrals. Look at problem 7.5.21.
7. 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".
8. 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.
9. Evaluate the integrals using the first fundamental theorem of calculus. Three parts. Look at problems 7.6.9-24.
10. Use the second fundamental theorem of calculus to find the derivative. Look at problems 7.6.45-50.
11. 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.
12. 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
13. Evaluate the definite integrals using substitution. Two parts. Look at problems 7.8.23-38
14. 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