Let be the region enclosed by and for

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

R

be the region enclosed by

x=4-y

and

x=y^{2}

for

0\le y\le\dfrac{-1+\sqrt{17}}{2}

. When

R

is revolved about the vertical line

x=-1

, which definite integral represents the volume of the resulting solid of revolution? (a)

\displaystyle \pi\int_{0}^{\frac{-1+\sqrt{17}}{2}}\Bigl[(5-y)^{2}-(y^{2})^{2}\Bigr]dy

(b)

\displaystyle \pi\int_{0}^{\frac{-1+\sqrt{17}}{2}}(5-y)^{2}\,dy

(c)

\displaystyle \pi\int_{0}^{\frac{-1+\sqrt{17}}{2}}\Bigl[(5-y)^{2}-(y^{2}+1)^{2}\Bigr]dy

(d)

\displaystyle \pi\int_{0}^{\frac{-1+\sqrt{17}}{2}}\Bigl[(y^{2}+1)^{2}-(5-y)^{2}\Bigr]dy