University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Practice Exercises - Page 474: 43

Answer

$4 \sqrt {2} |\sin(t/4)|+c$

Work Step by Step

Consider the integral $\int \sqrt {1+\cos (t/2)}dt$ The given integral can be re-written as: $\int \sqrt {1+(2\cos^2 (t/4)-1)}dt=\sqrt 2 \int \cos (t/4) dt$ This implies that $4 \sqrt {2 \sin^2(t/4)}+c=4 \sqrt {2} |\sin(t/4)|+c$
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