# Math 121 - Exam 5 Study Guide

1. A graph of a function is shown. Use rectangles to approximate the area under the curve. The function is not given, so the following problems are only vaguely like the one on the test. Look at problems 5.4.29-32 and 5.5.1-4.
2. Find the derivative and state a corresponding integration formula. Look at problems 5.2.3-6.
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 5.4.1-2.
5. Use the areas shown in the figure to find the definite integrals. Six parts. Look at problem 5.5.15.
6. Use part 2 of the fundamental theorem of calculus to evaluate the derivative. Look at problems 5.6.39-42.
7. Express the sum in closed form. Leave in factored form. Look at problems 5.4.17-20.
8. 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.
9. 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 5.7.53-54.
10. A particle moves along an s-axis. Use the given information to find the position function of the particle. Look at problems 5.7.7-10.
11. Evaluate the integrals. They may or may not require substitution. Four parts. Look at problems 5.2.9-28 and 5.3.5-30.
12. Evaluate the definite integrals. They may or may not require substitution. Five parts. Look at problems 5.6.7-19. and 5.8.3-12.

## Point values per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 5 4 4 6 12 4 5 5 5 5 20 25 100