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: 57



Work Step by Step

$\frac{dy}{dx}=cos(5x);$ $y(\pi)=3$ $dy=cos(5x)dx$ $\int dy=\frac{1}{5}\int5cos(5x)dx$ $y=\frac{1}{5}sin(5x)+C$ Substitute in the initial condition to solve for $C$ $3=\frac{1}{5}sin(5\pi)+C$ $C=3$ $y=\frac{1}{5}sin(5x)+3$
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