Mathematics

Problem

Region

A

is bounded above by

y=x

and below by the

x

-axis on

0\le x\le1

. Region

B

is bounded above by

y=1

and below by the

x

-axis on

1\le x\le2

. The union

A\cup B

is revolved about the

x

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

\dfrac{3\pi}{2}

\dfrac{8\pi}{3}

\dfrac{4\pi}{3}

\dfrac{\pi}{3}