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: 15

Answer

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

Work Step by Step

Setup the integration using shell method about the x-axis $2\pi \int_0^2 y(2-y)dy$ $ 2\pi \int_0^2 (2y-y^2)dy$ , Integrate $2\pi (y^2 -\frac{1}{3}y^3)]_0^2$ $2\pi(4-\frac{8}{3})$ $\frac{8\pi}{3}$
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