Mathematics

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

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

9\pi

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