Let R be the region in the first quadrant bounded by for

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

Problem

Let R be the region in the first quadrant bounded by

y=x

for

0\le x\le2

, by

y=2

for

2\le x\le3

, and by the x-axis. When R is revolved about the x-axis, what is the volume of the resulting solid? (a)

6\pi

(b)

\displaystyle \frac{20\pi}{3}

(c)

9\pi

(d)

\displaystyle \frac{14\pi}{3}