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Assignment 13-solutions

Assignment 13-solutions - nanni(arn437 Assignment 13...

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nanni (arn437) – Assignment 13 – guntel – (54940) 1 This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Evaluate the integral I = integraldisplay 1 / 2 0 sin - 1 x 1 - x 2 dx . 1. I = π 2 4 2. I = π 2 9 3. I = π 2 18 4. I = π 2 72 correct 5. I = π 2 8 Explanation: Set x = sin u . Then dx = cos u du, 1 - x 2 = cos 2 u , while x = 0 = u = 0 x = 1 2 = u = π 6 . In this case I = integraldisplay π 6 0 u cos u cos u du = integraldisplay π 6 0 u du . Consequently, I = bracketleftbigg u 2 2 bracketrightbigg π 6 0 = π 2 72 . 002 10.0points Determine the integral I = integraldisplay 1 ( x 2 + 4) 3 2 dx . 1. I = x 2 + 4 4 x + C 2. I = x x 2 + 4 + C 3. I = x 4 x 2 + 4 + C correct 4. I = 1 4 x 2 + 4 + C 5. I = x x 2 + 4 4 + C 6. I = x 2 + 4 x + C Explanation: Set x = 2 tan u. Then dx = 2 sec 2 u du , while ( x 2 + 4) 3 2 = ( 4(tan 2 u + 1) ) 3 2 = 8 sec 3 u . Thus I = integraldisplay 2 8 sec 2 u sec 3 u du = 1 4 integraldisplay cos u du , and so I = 1 4 sin u + C = 1 4 sin parenleftBig tan - 1 x 2 parenrightBig + C .
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