Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 90


$$\frac{\pi}{2}\left(e^{2}-1\right) $$

Work Step by Step

The volume of revolution about the $x-$ axis is given by \begin{aligned} V&=\pi \int_{a}^{b}f^2(x) d x \\ &=\pi \int_{0}^{1} e^{2 x} d x \\ &=\left.\pi \frac{e^{2 x}}{2}\right|_{0} ^{1} \\ &=\frac{\pi}{2}\left(e^{2}-1\right) \end{aligned}
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