Assignment 19-solutions

# Assignment 19-solutions - nanni(arn437 – Assignment 19...

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Unformatted text preview: nanni (arn437) – Assignment 19 – guntel – (54940) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Evaluate the integral I = integraldisplay 1 integraldisplay x 2 ( x- 2 y ) dydx . 1. I = 1 4 2. I = 3 20 3. I =- 1 20 4. I =- 3 20 5. I = 1 20 correct Explanation: After integration with respect to y we see that I = integraldisplay 1 bracketleftBig xy- y 2 bracketrightBig x 2 dx = integraldisplay 1 braceleftBig x 3- x 4 bracerightBig dx = bracketleftBig 1 4 x 4- 1 5 x 5 bracketrightBig 1 . Consequently, I = 1 4- 1 5 = 1 20 . 002 10.0 points Find the value of the double integral I = integraldisplay integraldisplay A (8 x- y ) dxdy when A is the region braceleftBig ( x, y ) : y ≤ x ≤ √ y, ≤ y ≤ 1 bracerightBig . 1. I = 1 2. I = 3 5 correct 3. I = 7 10 4. I = 4 5 5. I = 9 10 Explanation: The integral can be written as the repeated integral I = integraldisplay 1 bracketleftBigg integraldisplay √ y y (8 x- y ) dx bracketrightBigg dy. Now integraldisplay √ y y (8 x- y ) dx = bracketleftBig 4 x 2- xy bracketrightBig √ y y = 4 y- y 3 / 2- 3 y 2 ....
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Assignment 19-solutions - nanni(arn437 – Assignment 19...

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