Chapter 6: Applications of Definite Integrals - Section 6.2 - Volumes Using Cylindrical Shels - Exercises 6.2 - Page 330: 19

$\dfrac{ 4\pi}{3}$

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}^{1} (2 \pi) \cdot y (y-(-y)) dy$ Now, $V=[\dfrac{4 \pi y^3}{3}]_{0}^{1}$ or, $=\dfrac{ 4\pi}{3}$