University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 356: 42


$$\dfrac{108 \pi}{5}$$

Work Step by Step

We need to integrate the integral to compute the volume. We have: Area $=(R^2- r^2) \pi=\pi (12+4x-9x^2+x^4)$ Now, $$Volume= \pi \times \int_{-1}^{2} (12+4x-9x^2+x^4) \space dx \\= (24+8-24+(32/5)+12-2-3+\dfrac{1}{5}) \times \pi \\= \pi (15+\dfrac{33}{5} ) \\=\dfrac{108 \pi}{5}$$
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