Chapter 6: Applications of Definite Integrals - Section 6.2 - Volumes Using Cylindrical Shels - Exercises 6.2 - Page 329: 7

$8 \pi$

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)[x-\dfrac{-x}{2}] dx$ Now, $V=2 \pi \times \int_{0}^{2} [x^2] dx$ or, $= \pi \times [x^3]_{0}^{2}$ or, $=8 \pi$