test1ans-1practice

test1ans-1practice - Millersville University Name Answer...

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Unformatted text preview: Millersville University Name Answer Key Department of Mathematics MATH 211, Calculus II , Test 1 February 8, 2011 Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. 1. (15 points) Evaluate the following indefinite integral. 3 x cos 2 xdx Integrate by parts using u = 3 x du = 3 dx v = 1 2 sin 2 x dv = cos 2 xdx. Then 3 x cos 2 xdx = 3 2 x sin 2 x- 3 2 sin 2 xdx = 3 2 x sin 2 x + 3 4 cos 2 x + C 2. (15 points) Evaluate the following indefinite integral. cos 3 xdx Begin by factoring the integrand. cos 3 xdx = cos 2 x cos xdx = (1- sin 2 x ) cos xdx Integrate by substitution using u = sin x du = cos xdx then cos 3 xdx = (1- sin 2 x ) cos xdx = (1- u 2 ) du = u- 1 3 u 3 + C = sin x- 1 3 sin 3 x + C. 3. (15 points) Evaluate the following definite integral. Give an exact value, no decimal3....
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This note was uploaded on 03/20/2011 for the course MATH 211 taught by Professor Buchanan during the Spring '07 term at Millersville.

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test1ans-1practice - Millersville University Name Answer...

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