Answer
$y=-cos(x)+1$
Work Step by Step
$\frac{dy}{dx}=sin(x);$ $y(\frac{\pi}{2})=1$
$dy=sin(x)dx$
$\int dy=\int sin(x)dx$
$y=-cos(x)+C$
Substitute in the initial condition to solve for $C$
$1=-cos(\frac{\pi}{2})+C$
$C=1$
$y=-cos(x)+1$
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: 55
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