Answer
a) $\dfrac{9 \pi}{16}$; b) $\dfrac{9 \pi}{16}$
Work Step by Step
a) $V= \pi \int_{1/16}^{1} (x^{-1/4})^2)-(1)^2 dx=2 \pi \sqrt {x}-\pi y=\dfrac{9 \pi}{16}$
b) We need to use the shell model as follows:
$V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dx \\= \int_{1}^{2} (2 \pi) \cdot (y) (\dfrac{1}{y^4}-(/16)) \\=\dfrac{9 \pi}{16}$
