Answer
$L=\int_0^2\sqrt{1+(e^{-x})^2}dx=2.221$
Work Step by Step
$L=\int_a^b\sqrt{1+\Big(\frac{dy}{dx}\Big)^2}dx$
$y=1-e^{-x}$
$\frac{dy}{dx}=e^{-x}$
$a=0$; $b=2$
$L=\int_0^2\sqrt{1+(e^{-x})^2}dx=2.22141866594014
$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 8 - Section 8.1 - Arc Length - 8.1 Exercises - Page 549: 20
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