Answer
$$14 \pi $$
Work Step by Step
Consider the shell model to compute the volume:
$$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\=\int_1^{4} (2 \pi) \cdot (x)[\dfrac{3}{2 \sqrt x}] dx \\=3 \pi
\times \dfrac{x^{3/2}}{\frac{3}{2}}|_{1}^{4} \\=14 \pi $$