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: 3

Answer

$2 \pi$

Work Step by Step

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