Answer
$\dfrac{14 \pi }{3}$
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^{\sqrt 3} (2 \pi) \cdot (x)[\sqrt {x^2+1}) dx$
Suppose $a=x^2+1 \implies da=2xdx$
Now, $V= \pi \times \int_1^{4} [a^{1/2} da$
or, $=\pi \times [(2/3) a^{5/2}]_1^4$
or, $=\dfrac{14 \pi }{3}$
