Calculus (3rd Edition)

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: 56



Work Step by Step

$\frac{dy}{dz}=sin(2z);$ $y(\frac{\pi}{4})=4$ $dy=sin(2z)dz$ $\int dy=\int sin(2z)dz$ $y+C=\frac{1}{2}\int2sin(2z)dz$ $y=\frac{1}{2}(-cos(2z))+C$ Substitute in initial condition to solve for $C$ $4=\frac{-cos(\frac{\pi}{2})}{2}+C$ $4=C$ $y=\frac{-cos(2z)}{2}+4$
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