Math 134: Calculus 2 with Fundamentals Spring 2019 Exam 2 Information Department of Mathematics and Computer Science College of the Holy Cross

General Information

• The exam will be held on Tuesday, March 19, from 5:30pm to 7:00pm, in Swords 328.
• 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, 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.
• Continuously Compounded Interest, Present Value, Future Value. Know the formula for the balance of an account that earns interest compounded continuously. Also know the formulas for the present value and future value of a continuous income stream.
• Volumes of Revolution. (6.3) Know how to use disks and washers 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)tanⁿ(x), using either substitution if possible, or the two basic trigonometric identities and reduction formulas. The reduction formulas 44, 45, 46 and 48 in the back of the book will be provided, 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.
• Here are the guidelines for trigonometric integrals and trigonometric substitution that I handed out in class: Trig Integral Guidelines
• Partial Fractions. (7.5) 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.

Section 6.2, p. 348
Exercises 1, 5, 11, 13, 39, 41, 43, 45, 49, 51

Section 6.3, p. 356
Exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 27, 29, 31, 33, 35

Section 7.1, p. 377
Exercises 1, 3, 5, 11, 13, 17, 21, 23, 25, 35, 37, 39, 41, 43, 45, 47, 49, 51, 55, 57, 65, 77

Section 7.2, p. 384
Exercises 1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 29, 31, 35, 37, 39, 43, 49, 51, 53, 55, 57, 65

Section 7.3, p. 391
Exercises 1, 3, 7, 9, 11, 13, 15, 19, 25, 29, 37, 45

Section 7.5, p. 405
Exercises 7, 9, 13, 17, 25, 33, 35, 51

Here are some additional practice exercises: Practice Integrals, Solutions