University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.7 - Improper Integrals - Exercises - Page 471: 67

Answer

$$1$$

Work Step by Step

$$Area=\int_{0}^{\infty} e^{-x} dx \\=\lim\limits_{a \to \infty}\int_{0}^{a} e^{-x} dx \\=\lim\limits_{a \to \infty}[-e^{-x}]_{0}^a \\=\lim\limits_{a \to \infty}[-e^{-a}-(-e^{-1})] \\=0-(-1)=0+1\\=1$$
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