Answer
a.) $\displaystyle{V=2\pi\int_{0}^{1}\left(x+1\right)\left(\frac{2x}{1+x^3}-x\right)\ dx}\\ $
b.) $\displaystyle{V=2.36164}$
Work Step by Step
a.)
$\displaystyle{x=\frac{2x}{1+x^3}}\\
\displaystyle{x^4+x=2x}\\
\displaystyle{x^4-x=0}\\
\displaystyle{x\left(x^3-1\right)=0}\\
\displaystyle{x=0 \qquad x=1}\\$
$\displaystyle{V=\int_{0}^{1}\left(2\pi\left(x+1\right)\right)\left(\frac{2x}{1+x^3}-\left(x\right)\right)\ dx}\\
\displaystyle{V=2\pi\int_{0}^{1}\left(x+1\right)\left(\frac{2x}{1+x^3}-x\right)\ dx}\\ $
b.)
$\displaystyle{V=2.36164}$
