Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 6: Applications of Definite Integrals - Section 6.2 - Volumes Using Cylindrical Shels - Exercises 6.2 - Page 329: 4

Answer

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

Work Step by Step

We need to use the shell model as follows: $V=\int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dy$ $ \implies V= \int_0^{\sqrt 3} (2 \pi) \cdot (y)[3-(3-y^2) dy=2 \pi \times \int_0^{\sqrt 3} y^3 dy$ or, $=2\pi \times [\dfrac{y^4}{4}]_0^{\sqrt 3}$ or, $=\dfrac{9 \pi }{2}$
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