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 375: 23


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

Work Step by Step

$\displaystyle{A(x)=\pi(1)^{2}-\pi\left(x^{\frac{1}{4}}\right)^{2}}\\ \displaystyle{A(x)=\pi\left(1-x^{\frac{1}{2}}\right)}$ $\begin{aligned} V &=\int_{0}^{1} A(x) \ d x \\ V &=\int_{0}^{1} \pi\left(1-x^{\frac{1}{2}}\right) \ d x \\ V &=\pi \int_{0}^{1}1-x^{\frac{1}{2}} \ d x \\ V &=\pi\left[x-\frac{2}{3} x^{\frac{3}{2}}\right]_{0}^{1}\\ V &=\pi\left(\left(1-\frac{2}{3}(1)^{\frac{3}{2}} \right)-\left(0 \right)\right) \\ V &=\frac{\pi}{3} \end{aligned}$
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