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: 23

Answer

$8\pi$

Work Step by Step

Setup the integration using shell method about the line x=4 $ 2\pi \int _0^2 (4-x)(2x-x^2) dx$ $ 2\pi \int _0^2 (8x-4x^2 - 2x^2 +x^3)dx$ $2\pi \int_0^2 (x^3 - 6x^2 +8x)dx$, Integrate $2\pi [\frac{1}{4}x^4 - 2x^3 + 4x^2]_0^2$, Evaluate the definite integral $2\pi(4-16+16)$ $8\pi$
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