Answer
$ 2\pi(e^{3} -1)$
Work Step by Step
Setup the integration using disk method about the x-axis
$\pi \int_0^6 (e^{\frac{x}{4}})^2dx$
$\pi \int_0^6 e^{\frac{x}{2}}dx$, Integrate
$2\pi[e^{\frac{x}{2}}]_0^6$, Evaluate the definite integral
$ 2\pi(e^{3} -1)$
