Answer
a) $\tan^2 x; 0 \leq x \leq \pi/4$
b) $\dfrac{4 \pi-\pi^2}{2} $
Work Step by Step
a) $ x g(x) =x (\dfrac{\tan^2 x}{x})=\tan^2 x; 0 \leq x \leq \pi/4$
b) 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}^{\pi/4} (2 \pi) \cdot x (\dfrac{\tan^2 x}{x}) dx$
Now, $V=2 \pi (\tan x-x)_{0}^{\pi/4}$
or, $=2 \pi \times (\dfrac{4 -\pi}{4})$
or, $=\dfrac{4 \pi-\pi^2}{2} $
