Chapter 6.2, Problem 3QCE

A solid $S$ is generated by revolving the region enclosed by the line $y=2x+1$ and the curve $y=x^2+1$ about the $x\text{-axis}$ .

(a) For $x$ between $\text{\_\_\_\_\_\_\_}$ and $\text{\_\_\_\_\_\_\_}$ , the cross-sectional areal of $S$ perpendicular to the $x\text{-axis}$ at $x$ is $A\left(x\right)=\text{\_\_\_\_\_\_\_}$ .

(b) An integral expression for the volume of $S$ is $\text{\_\_\_\_\_\_\_\_}$ .