Answer
$$\pi$$
Work Step by Step
Consider the shell model to compute the volume:
$$V=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_0^{2} (2 \pi) \cdot (x)[2-2x^2] \space dx \\ =2 \pi [x^2-\dfrac{2x^4}{4}]_0^1\\=\pi$$