Answer
$6 \pi$
Work Step by Step
We need to use the shell model as follows:
$V=\int_0^{2} (2 \pi) \cdot x (1+\dfrac{x^2}{4}) dx$
or, $=2 \pi \times \int_0^{2} (x+\dfrac{x^3}{4}) dx$
or, $=pi \times (x^2/2+\dfrac{x^4}{16})_0^{2} dx$
or, $=6 \pi$
