Finding the volume of a solid bounded by curves.The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x = ( y − 9 ) 2 , x = 16 ; about y = 5I used the washer method in terms of y and got V = π ∫ 5 13 16 2 − ( y − 9 ) 2 d y = 8192 π 5 which is wrongAlso, I am having problems with another similar problem:The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. x = 1 − y 4 , x = 0 , about the line x = 5Any help on how to properly set up these integrals would be great, thank you.

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Finding the volume of a solid bounded by curves.The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.  x  =  (  y  −  9      )    2    ,  x  =  16  ;  about   y  =  5I used the washer method in terms of y and got  V  =  π      ∫    5          13            16    2    −  (  y  −  9      )    2    d  y  =            8192      π        5     which  is wrongAlso, I am having problems with another similar problem:The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.  x  =  1  −      y    4    ,  x  =  0  ,   about the line   x  =  5Any help on how to properly set up these integrals would be great, thank you.

Gemma Conley · Accepted Answer

Step 1If you want to use the washer method for the first problem, you have to solve for y in terms of x and then integrate with respect to x, since you are revolving around a horizontal line.It&#039;s easier to use the shell method, which gives      V    =          ∫      5              13              2    π    r    (    y    )    h    (    y    )        d    y    =          ∫      5              13              2    π    (    y    −    5    )    (    16    −    (    y    −    9          )      2        )        d    y  Step 2For the second problem, you could use the washer method to get      V    =          ∫              −        1                    1              π          (      (      R      (      y      )              )        2            −      (      r      (      y      )              )        2            )        d    y    =          ∫              −        1                    1              π          (              5        2            −      (      5      −      (      1      −              y        4            )              )        2            )        d    y    =    2          ∫      0      1        π          (              5        2            −      (      4      +              y        4                    )        2            )        d    y

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x=(y-9)^2, x=16; about y=5.

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