# Math 121 - Exam 5 Study Guide

1. A graph of a function is shown. Use either the left hand or right hand method (you'll be told which) of rectangles to approximate the area under the curve.
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. Find a closed form for the summation and simplify. Look at problems 5.4.17-20.
6. Simplify the limit of the summation. Look at problems 5.4.25-26.
7. Use the areas shown in the figure to find the definite integrals. Six parts. Look at problem 5.5.17-18.
8. Use part 2 of the fundamental theorem of calculus to evaluate the derivative. Look at problems 5.6.43-46.
9. 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.
10. 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.
11. Evaluate the indefinite integrals. Four parts.
12. Solve the initial value problem. Look at problems 5.2.37-38.
13. Evaluate the definite integrals. No substitution is needed. Four parts. Look at problems 5.6.7-22.
14. Use a u-substitution to rewrite the definite integrals and change the limits on the integrals. Do not evaluate the integrals. Two parts. Look at problems 5.8.1-2.
15. Evaluate the definite integral using either method of substitution. Look at problems 5.8.21-34.
16. Application problem involving rectilinear motion. Look at problems 5.7.27-34.

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total 4 3 3 6 4 4 12 4 4 4 16 4 16 8 4 4 100