The region enclosed by the curves ,

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

Problem

The region enclosed by the curves

x = y^{3}+1

x = 4

, and

y = 0

is revolved about the vertical line

x = -2

. What is the volume of the resulting solid? (a)

\displaystyle \pi\Bigl(3\cdot 3^{1/3}-\dfrac{3^{4/3}}{4}\Bigr)

(b)

\displaystyle \frac{297\pi}{14} \,3^{1/3}

(c)

\displaystyle \pi\Bigl(15\cdot 3^{1/3}-\tfrac12\,3^{4/3}-\tfrac{3^{7/3}}{7}\Bigr)

(d)

\displaystyle \frac{57\pi}{14}\,3^{4/3}