The region \(R\) bounded by the curves \(x=y^{2}\) and \(x-2y=15\) is revolved about the line \(x=-2\).
To use the Washer Method to set up an integral or sum of integrals that would give the volume of the solid:
we should integrate with respect to \(x\). we should integrate with respect to \(y\).
How many integrals will we need to express the volume of the solid using the Washer Method: \(\answer {1}\)
Express the volume of the solid using the Washer Method:
\[ V=\int _{\answer {-3}}^{\answer {5}} \answer {\pi \left (2+2y+15 \right )^{2}-\pi \left ( 2+y^{2}\right )^{2}} \d y \]
To use the Shell Method to set up an integral or sum of integrals that would give the volume of the solid:
we should integrate with respect to \(x\). we should integrate with respect to \(y\).
How many integrals will we need to express the volume of the solid using the Shell method: \(\answer {2}\).
Express the volume of the solid using the Shell Method:
\[ V=\int _{\answer {0}}^{\answer {9}} \answer {2\pi \left ( 2+x \right ) \left (2 \sqrt {x} \right )} \d x + \int _{\answer {9}}^{\answer {25}} \answer { 2\pi \left ( 2 +x \right ) \left ( \sqrt {x} - \frac {1}{2}\left ( x -15 \right ) \right ) } \d x \]
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