The curve encloses a region with the -axis between and

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

Problem

The curve

y = x^{3}+1

encloses a region with the

y

-axis between

y=1

and

y=9

. This region is rotated about the

y

-axis to form a solid. What is the exact volume of the solid? (a)

32\pi

(b)

\dfrac{84\pi}{5}

(c)

\dfrac{96\pi}{5}

(d)

12\pi