Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 7 - Applications of Integration - 7.2 Exercises: 5

Answer

$$V=\frac{6\pi}{55}$$

Work Step by Step

$V=\pi\int_0^1 (x^2)^2-(x^5)^2dx$ $V=\pi\int_0^1 (x^4-x^{10}) dx$ $V=\pi[\frac{x^5}{5}-\frac{x^{11}}{11}]_0^1$ $V=\pi [(\frac{1^5}{5}-\frac{1^{11}}{11})-(\frac{0^5}{5}-\frac{0^{11}}{11})]$ $V=\pi[(\frac{1}{5}-\frac{1}{11})-(0)]$ $V=\pi(\frac{11}{55}-\frac{5}{55})$ $V=\frac{6\pi}{55}$
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