Mathematics

Problem

Let

R

be the region bounded by the x-axis and the graph of the piecewise function

p(x)=\begin{cases}x^2,&0\le x\le 1\\2x-1,&1<x\le 2\end{cases}.

When

R

is revolved about the x-axis, what is the volume of the resulting solid? a)

\dfrac{96\pi}{15}

\dfrac{68\pi}{15}

\dfrac{35\pi}{15}

\dfrac{63\pi}{15}