Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 97

Answer

$V= \frac{\pi}{2}(e^{2}-1)=10.0359$

Work Step by Step

The volume of the solid obtained by rotating the region under the curve $y=e^{x}$ From 0 to 1 about the x-axis is equal to $V=\int_{0}^{1} A(x) dx$ $=\int_{0}^{1} \pi e^{2x} dx$ $=\pi(\frac{e^{2x}}{2})_{0}^{1}$ Hence, $V= \frac{\pi}{2}(e^{2}-1)=10.0359$
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