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: 7

Answer

$\frac{16\pi}{3}$

Work Step by Step

Setup the integration using shell method about the y-axis. Setup the integration using Shell Method $ 2\pi \int_0^2 x((4x-x^2) - x^2)dx$ $ 2 \pi \int_0^2 (4x^2 - 2x^3)dx $ ,Bring a factor of 2 out $ 4\pi \int_0^2 (2x^2 - x^3)dx$ $ 4\pi (\frac{2}{3} x^3 - \frac{1}{4} x^4)]_0^2 $, Integrate $ 4\pi ( \frac{16}{3} -4) -0 $, Take Definite Integral $\frac{16\pi}{3}$
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