Answer
$\dfrac{7\pi}{15}$
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^{1} (2 \pi) \cdot (x)[\sqrt x-(2x-1)] dx$
Now, $V=2 \pi [(2/5)x^{5/2}-(2/3)x^3+\dfrac{x^2}{2}]_0^1$
or, $= 2 \pi \times (\dfrac{2}{5}-\dfrac{2}{3}+\dfrac{1}{2})$
or, $=\dfrac{7\pi}{15}$
