Math 136: Calculus 2 Spring 2017 Exam 2 Information Department of Mathematics and Computer Science College of the Holy Cross

General Information

• The exam will be held on Thursday, March 23, from 5:30pm to 7:00pm, in Smith Labs 154.
• Plan to arrive a few minutes early to allow time to distribute the exams.
• The exam will cover material from sections 6.2, 6.3, 6.4, 7.1, 7.2, 7.3, and 7.5 in the text.
• Cell-phones should be turned OFF for the duration of the exam.
• You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
• This is a closed-book exam. No books or notes may be used during the exam.
• You will be expected to show all of your work. A correct answer with insufficient justification may not receive full credit.

Topics

• Volumes and Average Value. (6.2) Be able to use formula (1) to find the volume of a solid by determining the cross-sectional area function and integrating it. Also know formula (6) for the average value of a function.
• Volumes of Revolution. (6.3 and 6.4) Know how to use disks, washers, and cylindrical shells to find the volume of a solid of revolution.
• Integration by Parts. (7.1) Know how to use integration by parts to evaluate a given integral. Remember LIPET for the choice of u.
• Trigonometric Integrals. (7.2) You should be able to integrate any function of the form sin^m (x)cosⁿ(x) or sec^m(x)tsnⁿ(x), using either substitution if possible, or the two basic trigonometric identities and reduction formulas. I will provide the reduction formulas 44, 45, 46 and 48 in the back of the book, but you should know the integrals of sec(x) and tan(x).
• Trigonometric Substitution. (7.3) Know how to use a trigonometric substitution to evaluate integrals involving a²-x², x²-a², and a²+x².
• Partial Fractions. (7.4) Know how to use the partial fractions method to evaluate rational functions where the denominator has some number of linear factors (possibly repeated), as well as irreducible quadratic factors (but not repeated).
• Completing the Square. Some of the trigonometric substitution and partial fractions problems may require you to complete the square. See pages 16 and 17 in the text.

Preparing for the Exam

Here are a some problems from the Chapter Review sections to use for practice. Solutions to the odd-numbered exercises are in the back of the text.

Chapter 6 Review, p. 371
Exercises 14, 16, 19-40

Chapter 7 Review, p. 440
Exercises 1-29, 34-38, 41-43, 45-54, 56-57, 63