Math 121 - Chapter 5 Study Guide

1. Use a simple formula from geometry to find the area function A(x) that gives the area of the graph of the function on the interval. Look at problems 5.1.9-14.
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 indefinite integrals. Three parts. Look at problems 5.2.9-28
5. Evaluate the summation. Two parts. Look at problems 5.4.1-2.
6. Evaluate the integrals by making appropriate substitutions. Three parts. Look at problems 5.3.5-30.
7. Write the expression in sigma notation, but do not evaluate. Two parts. Look at problems 5.4.3-8.
8. Use the areas shown in the figure to find the definite integrals. Five parts. Look at problem 5.5.15.
9. Use part 2 of the fundamental theorem of calculus to evaluate the derivative. Look at problems 5.6.39-42.
10. Express the sum in closed form. Look at problems 5.4.17-20.
11. Find a polynomial function with 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. Use the y-intercept as an initial value.
12. Sketch the region whose signed area is represented by the definite integral, and evaluate the integral using an appropriate formula from geometry. Look at problems 5.5.11-14.
13. 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.
14. Evaluate the integrals using the first fundamental theorem of calculus. Three parts. Look at problems 5.6.7-19.
15. Evaluate the definite integrals using substitution. Three parts. Look at problems 5.8.3-12.
16. 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.
17. 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 5.7.15-18.

Notes:

• Some of the problems are directly from the text.