Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 5 - Applications of Integration - 5.2 Volumes - 5.2 Exercises - Page 374: 19


$\displaystyle{V=\frac{\pi }{3}}\\ $

Work Step by Step

$\displaystyle{A\left(x\right)=\pi \left(x\right)^2}\\ \displaystyle{A\left(x\right)=\pi \left(x^2\right)}\\$ $\displaystyle{V=\int_{0}^{1}A\left(x\right)\ dx}\\ \displaystyle{V=\int_{0}^{1}\pi \left(x^2\right)\ dx}\\ \displaystyle{V=\pi \int_{0}^{1}x^2\ dx}\\ \displaystyle{V=\pi\left[\frac{1}{3}x^3\right]_{0}^{1}}\\ \displaystyle{V=\pi\left(\frac{1}{3}(1)^3-\frac{1}{3}(0)^3\right)}\\ \displaystyle{V=\frac{\pi }{3}}\\ $
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