Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 6 - Section 6.2 - Volume - 6.2 Exercises - Page 456: 29

Answer

$\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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