Answer
a) $$\dfrac{9 \pi}{16}$$
b) $$\dfrac{9 \pi}{16}$$
Work Step by Step
a) $$Volume= (\pi) \int_{1/16}^{1} (x^{-1/4})^2)-(1)^2 \space dx \\=2 \pi \sqrt {x}-\pi y \\=\dfrac{9 \pi}{16}$$
b) Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= (2 \pi) \int_{1}^{2}(y) (\dfrac{1}{y^4}-\dfrac{1}{16}) \\=\dfrac{9 \pi}{16}$$
