Answer
a.) $\displaystyle{V=2\pi\int_{0}^{2}x^2e^{-x}\ dx}\\ $
b.) $\displaystyle{V=4.06300}$
Work Step by Step
a.)
$\displaystyle{V=\int_{0}^{2}(2\pi x)\left(xe^{-x}\right)\ dx}\\
\displaystyle{V=2\pi\int_{0}^{2}x^2e^{-x}\ dx}\\ $
b.)
$\displaystyle{V=4.06300}$
