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Assignment 15-solutions

# Assignment 15-solutions - nanni(arn437 Assignment 15...

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nanni (arn437) – Assignment 15 – guntel – (54940) 1 This print-out should have 4 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 π/ 4 0 sec 2 x (1 - 4 sin x ) dx . 1. I = 5 + 4 2 2. I = - 3 - 4 2 3. I = - 3 - 4 2 4. I = 5 + 4 2 5. I = - 3 + 4 2 6. I = 5 - 4 2 correct Explanation: Since sec 2 x { 1 - 4 sin x } = sec 2 x - 4 sec x parenleftBig sin x cos x parenrightBig , we see that I = integraldisplay π/ 4 0 { sec 2 x - 4 sec x tan x } dx . But d dx tan x = sec 2 x , while d dx sec x = sec x tan x . Consequently, I = bracketleftBig tan x - 4 sec x bracketrightBig π/ 4 0 = 5 - 4 2 . 002 10.0points Determine the integral I = integraldisplay x 2 + 1 x - 1 dx . 1. I = x 2 + x - ln | x - 1 | + C 2. I = 1 2 x 2 + x + 2 ln | x - 1 | + C correct 3. I = x 2 + x - ln | x + 1 | + C 4. I = 1 2 x 2 + x - 2 ln | x - 1 | + C 5. I = 1 2 x 2 - x + 2 ln | x + 1 | + C 6. I = x 2 - x - ln | x + 1 | + C Explanation: After division x 2 + 1 x - 1 = ( x 2 - 1) + 2 x - 1 = x 2 - 1 x - 1 + 2 x - 1 = x + 1 + 2 x - 1 .

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Assignment 15-solutions - nanni(arn437 Assignment 15...

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