Answer
$\displaystyle{V=14.450}$
Work Step by Step
$\displaystyle{V=\int_{0}^{2.175}(2\pi x)\left(\frac{x}{x^{2}+1}-\left(x^{2}-2x\right)\right)\ dx}\\
\displaystyle{V=2\pi\int_{0}^{2.175}\frac{x^2}{x^{2}+1}-x^{3}+2x^2\ dx}\\
\displaystyle{V=14.450}$