math11 - Math 2153, Exam I, Feb. 17, 2010 Name: Score: Read...

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Unformatted text preview: Math 2153, Exam I, Feb. 17, 2010 Name: Score: Read the problems carefully before you begin. Show all your work neatly and concisely, and indicate your final answer clearly. Total points = 50. 1. (8 points) Evaluate the integral integraltext ( x 2 + 1) e x dx Solution 1 Use integration by parts twice: integraldisplay ( x 2 + 1) e x dx parenleftbigg set u = x 2 + 1 v = e x u = 2 x v =- x x parenrightbigg =( x 2 + 1)(- e x )- integraldisplay 2 x (- e x ) dx ( simplify ) =- ( x 2 + 1) e x + integraldisplay 2 xe x dx parenleftbigg set u = 2 x v = e x u = 2 v =- e x parenrightbigg =- ( x 2 + 1) e x + bracketleftbigg 2 x (- e x )- integraldisplay 2(- e x ) dx bracketrightbigg ( simplify ) =- ( x 2 + 1) e x- 2 xe x + integraldisplay 2 e x dx =- ( x 2 + 1) e x- 2 xe x- 2 e x + C Solution 2 Use tabular integration by parts: We have integraldisplay ( x 2 + 1) e x dx =- ( x 2 + 1) e x- 2 xe x- 2 e x + C 1 2. (8 points) Evaluate the integral integraltext sin 2 x cos 5 x dx Solution Using the identity...
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This note was uploaded on 09/22/2011 for the course MATH 2153 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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math11 - Math 2153, Exam I, Feb. 17, 2010 Name: Score: Read...

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