## Calculus 10th Edition

Published by Brooks Cole

# Chapter 7 - Applications of Integration - 7.2 Exercises: 27

#### Answer

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

#### Work Step by Step

Setup the integration using disk method about the x-axis $\pi \int_0^1 (e^{-x})^2dx$ $\pi \int_0^1 (e^{-2x})dx$, integrate $-\frac{\pi}{2}[e^{-2x}]_0^1$, evaluate the definite integral $-\frac{\pi}{2}(e^{-2} -1)$ $\frac{\pi}{2}(1-\frac{1}{e^2})$, simplify

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