Answer
$y=-e^{-t}+1$
Work Step by Step
$\frac{dy}{dt}=e^{-t};$ $y(0)=0$
$\int dy=-\int-e^{-t}dt$
$y=-e^{-t}+C$
Substitute in the initial condition to solve for $C$
$0=-e^{-0}+C$
$C=1$
$y=-e^{-t}+1$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises - Page 253: 60
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