Mathematics

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}

\dfrac{176\pi}{3}

\dfrac{128\pi}{3}

\dfrac{80\pi}{3}