Math 136: Calculus 2 Spring 2018 Exam 1 Information

Department of Mathematics and Computer Science
College of the Holy Cross

General Information

• The exam will be held on Tuesday, February 20, 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 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, and 6.1 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

• Approximating Areas. (5.1) Know how to set up and calculate summations for RN, LN and MN. Know how to use Theorem 1 to compute the exact area under the graph of a function. Also know the power sum formulas (3), (4) and (5).
• Definite Integrals. (5.2) Know the definition of the definite integral as a limit of Riemann sums (p. 273). Know how to interpret definite integrals as signed are and be able to use this to compute definite integrals. Know the basic properties of integrals in Theorems 2, 3, 4 and 5.
• Indefinite Integrals. (5.3) Know the definition of an antiderivative of a function and the indefinite integral of a function. Know all the basic antiderivative formulas (power rule, trigonometric integrals and exponentials) and the basic properties of indefinite integrals in Theorem 4. Be able to use indefinite integrals to solve initial value problems.
• Fundamental Theorem of Calculus. (5.4) and (5.5) Know the precise statement of the Fundamental Theorem of Calculus, Part I (Theorem 1, p. 289). Know how to use FTC I to calculate definite integrals. Know the precise statement of the Fundamental Theorem of Calculus, Part II (Theorem 1, p. 295). Be able to use FTC II to evaluate derivatives of functions defined by definite integrals, and to write down solutions of initial value problems in terms of functions defined by definite integrals.
• Net Change. (5.6) Know how to use Theorem 1 to find the net change of function given its rate of change. Be able to interpret the net change of a function s(t) in terms of areas between its derivative s'(t) and the t-axis. Understand the difference between net displacement and total distance travelled, and know how to set up integrals to calculate each of these.
• Substitution. (5.7) Know how to use substitution to evaluate definite and indefinite integrals.
• Other Transcendental Functions. (5.8) Know the antiderivate formulas (1), (2), (3), (4) and (5).
• Area Between Curves. (6.1) Know how to set up and evaluate integrals to calculate the area of a given region.

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 5 Review, p. 329
Exercises 1-2, 4-11, 13-93, 96-97, 105, 107-113

Chapter 6 Review, p. 371
Exercises 1-7, 9-11