Answer
$6 \pi$
Work Step by Step
We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx$
$ \implies V= \int_0^{2} (2 \pi) \cdot x (2-\dfrac{x^2}{4}) dx=2 \pi \times \int_0^{2} (2x-\dfrac{x^3}{4}) dx$
or, $=2\pi \times [x^2-\dfrac{x^4}{16}]_0^{2} $
or, $=6 \pi$
