Mathematics

Problem

The region in the first quadrant is bounded above by

y=x^{2}

for

0\le x\le2

and by

y=4

for

2< x\le3

, and is bounded below by the

x

-axis on the entire interval

0\le x\le3

. Determine the exact volume of the solid obtained when this region is revolved about the

x

-axis.