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: 1


$6 \pi$

Work Step by Step

We need to use the shell model as follows: $V=\int_0^{2} (2 \pi) \cdot x (1+\dfrac{x^2}{4}) dx$ or, $=2 \pi \times \int_0^{2} (x+\dfrac{x^3}{4}) dx$ or, $=pi \times (x^2/2+\dfrac{x^4}{16})_0^{2} dx$ or, $=6 \pi$
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