University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.2 - Volumes Using Cylindrical Shells - Exercises - Page 364: 15


$$\dfrac{16 \pi (3\sqrt 2+5)}{15}$$

Work Step by Step

Consider the shell model to compute the volume: $$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_{0}^{2} (2 \pi) \cdot y (\sqrt y-(-y)) dy \\ =2 \pi \times [\dfrac{2y^2}{5}\sqrt y+\dfrac{y^2}{3}]_{0}^{2} \\=\dfrac{16 \pi (3\sqrt 2+5)}{15}$$
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