A region is bounded above by the piecewise function f(x)= cases 2x+1,&0 x 2 5,&2<x 3…

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

Problem

A region is bounded above by the piecewise function

f(x)=\begin{cases}2x+1,&0\le x\le 2\\5,&2<x\le 3\end{cases}

and below by the line

y=1

. The region is revolved about the horizontal line

y=-1

. What is the volume of the solid formed? (a)

\dfrac{212\pi}{3}

(b)

\dfrac{176\pi}{3}

(c)

\dfrac{128\pi}{3}

(d)

\dfrac{80\pi}{3}