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prob7 - Math 151 Spring 2008 Problem Set 7 Volumes Length...

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Math 151 Spring 2008 Problem Set # 7: Volumes, Length and Surface Area Starred Problems are due on Friday, March 7 Volumes by Slices or Cylindrical Shells In problems 1-4, use the method of disks to determine the volume of the solid that is obtained by revolving the region between the graph of z = f ( x ) and the given interval about the x -axis. 1*. f ( x ) = e x ; [ ln (2) , ln (2)] 2. f ( x ) = sin ³ x 4 ´ ; [2 π, 3 π ] 3. f ( x ) = r x x 2 + 4 ; h p e 2 4 , p e 3 4 i 4*. f ( x ) = r 1 x 2 + 1 , [ 1 , 1] . In problems 5 and 6, use the method of washers to determine the volume of the solid that is obtained by revolving the region between the graphs of z = f ( x ) , z = g ( x ) , x = a and x = b about the x -axis. 5. f ( x ) = 1 x , g ( x ) = 1 x 2 , x = 1 , x = 2 . 6*. f ( x ) = sin ( x ) , g ( x ) = cos ( x ) , x = π/ 4 , x = π/ 2 In problems 7-10, use the method of cylindrical shells to determine the volume of the solid that is obtained by revolving the graph of z = f ( x ) on the given interval about the z -axis. 7. f ( x ) = sin ¡ x 2 ¢ , r π 6 , r π 4 ¸ 8*.
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