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: 16


$$\dfrac{40 \pi}{3}$$

Work Step by Step

Consider the shell model to compute the volume: $$Volume=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_{0}^{2} (2 \pi) \cdot y (y^2-(-y)) dy \\=2 \pi \times (\dfrac{y^4}{4}+\dfrac{y^3}{3})_{0}^{2} \\=\dfrac{40 \pi}{3}$$
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