Chapter 6: Applications of Definite Integrals - Section 6.2 - Volumes Using Cylindrical Shels - Exercises 6.2 - Page 329: 10

$\pi$

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^{2} (2 \pi) \cdot (x)[2-2x^2] dx$ Now, $V=2 \pi [x^2-\dfrac{2x^4}{4}]_0^1$ or, $= 2 \pi \times (1-\dfrac{1}{2})$ or, $=\pi$