A region in the xy-plane is bounded above by the piecewise function h(x)= cases 2x,&0…

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

Problem

A region in the xy-plane is bounded above by the piecewise function

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

and below by the x-axis. The region is revolved about the horizontal line

y=-1

. On the sub-interval

0\le x\le 1

, which of the following ordered pairs gives the squared outer radius

R_{\text{out}}^{\,2}(x)

and squared inner radius

R_{\text{in}}^{\,2}(x)

required to compute the volume of the solid? (a)

\bigl((2x)^2,\;1\bigr)

(b)

\bigl((2x+1)^2,\;1\bigr)

(c)

\bigl((2x+1)^2,\;(2x)^2\bigr)

(d)

\bigl((2x+1)^2,\;0\bigr)