Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.