Region is bounded above by and below by the -axis on

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

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}

(b)

\dfrac{8\pi}{3}

(c)

\dfrac{4\pi}{3}

(d)

\dfrac{\pi}{3}