Region consists of two subregions: • For

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

Problem

Region

R

consists of two subregions: • For

0\le y\le1

, the region is bounded by

x=y^2

and the

y

-axis. • For

1\le y\le2

, the region is bounded by

x=y

and the

y

-axis. The entire region

R

is revolved about the

y

-axis. What is the volume of the solid generated? (a)

\dfrac{32\pi}{15}

(b)

\dfrac{40\pi}{15}

(c)

\dfrac{38\pi}{15}

(d)

\dfrac{35\pi}{15}