# Math 122: Chapter 8 Study Guide

1. Evaluate the integral using integration by parts.
2. Evaluate the integral using the tabular method of integration by parts.
3. Evaluate the trigonometric integral.
4. Evaluate the trigonometric integral.
5. Integrate using a trigonometric substitution.
6. Integrate using partial fractions.
7. Integrate using partial fractions. You should be aware of how to handle improper fractions.
8. Evaluate the improper integral.
9. Evaluate the improper integral.
10. Approximate the area under the curve using the Trapezoid Rule and Simpson's Rule.
11. Find the derivative. Three parts. From chapter 7.
12. Find the limit. Two parts. From chapter 7.
13. Find the number of sub-intervals necessary to guarantee the specified accuracy in the approximation to the integral. The appropriate error formula is given on the test.
14. Find the integral. Five parts. Three of these are from chapter 7. For the two in chapter 8, pay attention to the special integrals using rational exponents in section 8.6 and those that require completing the square from section 8.4.

## Notes

• There is a take home portion of the exam worth 60 points.
• The in-class portion of the test must be worked without a computer.
• The in-class portion of the exam is worth 65 points.
• Although the in-class portion is only worth 65 points, there are 74 points possible. However, the test is a little longer than I would like, so I am planning on people not being able to answer all of it. You can miss some problems and still get a "perfect" score.
• You will need data from the USGS Water Data site to answer question 1 on the take home.
• The take home exam is due the day of the in-class exam.
• From chapter 7, you should know the derivatives of the inverse trigonometric functions, the integrals resulting in inverse trigonometric forms, and the derivatives of the hyperbolic trigonometric functions.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 take home Total 4 4 4 4 4 4 4 4 4 4 9 6 4 15 60 125