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 - 7.3 Exercises: 9

Answer

$\frac{8\pi}{3}$

Work Step by Step

Setup the integration using shell method about the y-axis $ 2\pi \int_0^2 x(4-(4x-x^2))dx$ $ 2\pi \int_0^2 (4x-4x^2 +x^3)dx$, Integrate $2\pi (2x^2 - \frac{4}{3}x^3 + \frac{1}{4}x^4)]_0^2 $, Take the definite integral $2\pi(8-\frac{32}{3} +4)-0$ $\frac{8\pi}{3}$
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