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

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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 10.0points 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 π 2. V = 3 5 π 3. V = 1 5 π 4. V = 3 10 π correct 5. V = 1 2 π 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 = π integraldisplay 1 0 braceleftBig ( x 1 / 2 ) 2 - ( x 2 ) 2 bracerightBig dx = π integraldisplay 1 0 braceleftBig x 1 - x 4 bracerightBig dx = π bracketleftbigg 1 2 x 2 - 1 5 x 5 bracketrightbigg 1 0 . Consequently, V = π parenleftBig 1 2 - 1 5 parenrightBig = 3 10 π . 002 10.0points 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 π 5 2. V = 3 π 4 3. V = 7 π 15 4. V = 3 π 5 5. V = 29 π 30 correct 6. V = 9 π 10 7. V = π 2 8. V = 31 π 30 Explanation: The region enclosed by the graphs of x = y, x = y 2 ,
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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 line x = - 1 let’s see first what a horizontal cross-section of the solid looks like. As shown
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