## Math 190 - Chapter 6 Study Guide

1. Find the indefinite integrals. Don't forget the constant of integration. Some of the problems will require substitution. Five parts. Look at problems 6.1.9 - 6.1.47 and 6.2.1 - 6.2.39.
2. Find the definite integrals. Some of the problems will require substitution. Five parts. Look at problems 6.4.17 - 6.4.39 and 6.5.1 - 6.5.27.
3. Approximate the area under a curve using a Riemann sum. In each case, sketch the rectangles being used, list the points (x-values) and the heights (y-values) and give the approximate area. Use the left-hand endpoints, right-hand endpoints, and midpoints, of the intervals. Also find a numerical approximation using the numerical integration capabilities of your graphing calculator. Four parts. Look at problems 6.3.7b, 6.3.8b, and 6.3.9b. This is the only problem on the test that is not exactly from the textbook.
4. Find the average value of the given function on the indicated interval. Look at problems 6.5.29 - 6.5.37.
5. Sketch the graphs of the function and find the area between them over the given interval. Look at problems 6.6.17 - 6.6.25.

### Notes

• Except for problem 3, all problems are directly from the textbook.
• Problem 3 is similar to a problem from the textbook, but the function and number of intervals is different.
• There is a take home portion of the test worth 16 points. It covers Consumer's / Producer's surplus problems and Lorentz Curve problems. The take home exam will be given out with the exam and will be due the following class period.
 # 1 2 3 4 5 Total Points 30 30 12 6 6 84