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 363: 4


$$\dfrac{9 \pi }{2}$$

Work Step by Step

Consider the shell model to compute the volume: $$V=\int_{m}^{n} (2 \pi) (\space Radius \space of \space shell) \times ( height \space \text{of} \space \text {shell}) dx \\= \int_0^{\sqrt 3} (2 \pi) \cdot (y)[3-(3-y^2) dy \\=2 \pi \times \int_0^{\sqrt 3} y^3 dy \\=2\pi \times [\dfrac{y^4}{4}]_0^{\sqrt 3} \\=\dfrac{9 \pi }{2}$$
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