Answer
a) $\sin x; 0 \leq x \leq \pi$, b) $4 \pi $
Work Step by Step
a) $ x f(x) =x (\dfrac{\sin x}{x})=\sin x; 0 \leq x \leq \pi$
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} (2 \pi) \cdot (x)[\dfrac{\sin x}{x}] dx$
Now, $V=2 \pi [-\cos x]_{0}^{\pi}$
or, $=-2 \pi \times (-1-1)$
or, $=4 \pi $
Thus, the answers are:
a) $\sin x; 0 \leq x \leq \pi$
b) $4 \pi $
