Assignment 6-solutions

Assignment 6-solutions - nanni (arn437) – Assignment 6...

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Unformatted text preview: nanni (arn437) – Assignment 6 – guntel – (54940) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the definite integral I = integraldisplay π/ 4 (5 cos2 x + 3 sin2 x ) dx . 1. I = 5 2. I = 6 3. I = 7 4. I = 3 5. I = 4 correct Explanation: To reduce the integral to one involving just cos u and sin u set u = 2 x . Then du = 2 dx , while x = 0 = ⇒ u = 0 , and x = π 4 = ⇒ u = π 2 . In this case, I = 1 2 integraldisplay π/ 2 (5 cos u + 3 sin u ) du = 1 2 bracketleftBig 5 sin u- 3 cos u bracketrightBig π/ 2 . But sin π 2 = 1 , sin 0 = 0 , while cos π 2 = 0 , cos 0 = 1 . Consequently, I = 1 2 (5- (- 3)) = 4 . keywords: IntSubst, IntSubstExam, 002 10.0 points Evaluate the integral I = integraldisplay 1 2 x (2- x 2 ) 2 dx . 1. I = 3 2. I = 10 3 3. I = 7 3 correct 4. I = 8 3 5. I = 2 Explanation: Set u = 2- x 2 . Then du =- 2 x , while x = 0 = ⇒ u = 2 , x = 1 = ⇒ u = 1 . Thus I =- integraldisplay 1 2 u 2 du = integraldisplay 2 1 u 2 du = 1 3 bracketleftBig u 3 bracketrightBig 2 1 ....
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This note was uploaded on 09/19/2011 for the course M 408 taught by Professor Hodges during the Fall '08 term at University of Texas.

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Assignment 6-solutions - nanni (arn437) – Assignment 6...

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