Assignment 8-solutions - nanni (arn437) Assignment 8 guntel...

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Unformatted text preview: nanni (arn437) Assignment 8 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 Find the volume, V , of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of y = x 2 , x = y 2 about the x-axis. 1. V = 2 5 2. V = 3 5 3. V = 1 5 4. V = 3 10 correct 5. V = 1 2 Explanation: Since the graphs of y = x 2 , x = y 2 intersect in the first quadrant at (0 , 0) and at (1 , 1) the bounded region in the first quad- rant enclosed by their graphs is the shaded area shown in 1 1 Thus the volume of the solid of revolution generated by rotating this region about the x-axis is given by V = integraldisplay 1 braceleftBig ( x 1 / 2 ) 2- ( x 2 ) 2 bracerightBig dx = integraldisplay 1 braceleftBig x 1- x 4 bracerightBig dx = bracketleftbigg 1 2 x 2- 1 5 x 5 bracketrightbigg 1 . Consequently, V = parenleftBig 1 2- 1 5 parenrightBig = 3 10 . 002 10.0 points Find the volume, V , of the solid obtained by rotating the region bounded by the graphs of x = y 2 , x = y about the line x =- 1. 1. V = 2 5 2. V = 3 4 3. V = 7 15 4. V = 3 5 5. V = 29 30 correct 6. V = 9 10 7. V = 2 8. V = 31 30 Explanation: The region enclosed by the graphs of x = y, x = y 2 , nanni (arn437) Assignment 8 guntel (54940) 2 is the shaded region in y x x = y : x = y 2 : (1 , 1) To determine the volume of the solid gener- ated when this region is rotated about the...
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This note was uploaded on 11/02/2011 for the course CALCULUS 408S taught by Professor Guntel during the Fall '11 term at University of Texas at Austin.

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Assignment 8-solutions - nanni (arn437) Assignment 8 guntel...

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