Finding the volume of revolution using the method of shellsI'm trying to find the volume of the solid generated by revolving the region bounded by y = x 2 and y = 6 x + 7 about x-axis using the shell method. I applied the method and I got 15864/5 multiplied by π but it's not correct.Details: I integrated ∫ 1 49 y ( y − y − 7 6 ) d y

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Finding the volume of revolution using the method of shellsI&#039;m trying to find the volume of the solid generated by revolving the region bounded by   y  =      x    2   and   y  =  6  x  +  7 about x-axis using the shell method. I applied the method and I got 15864/5 multiplied by   π but it&#039;s not correct.Details: I integrated       ∫          1              49        y  (      y    −            y      −      7        6    )  d  y

Tamia Campbell · Accepted Answer

Explanation:If you want to use the shell method, then you would need             ∫      0              1              2    π    y          (              y            −      (      −              y            )      )        d    y    +          ∫              1                    49              2    π    y          (              y            −                        y          −          7                6            )        d    y  ; but using the disc method.

vroos5p · Accepted Answer

Explanation:For revolving about the x-axis, use washers. Then   V  =  π      ∫          −      1        7    [  (  6  x  +  7      )    2    −  (      x    2        )    2    ]  d  x

Find the volume of the solid generated by revolving the region bounded by y=x^2 and y=6x+7 about x-axis using the shell method.

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