Answer
$A=\sqrt 2-1$
Work Step by Step
$A=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(sin(x)-cos(x))dx$
$A=[-cos(x)-sin(x)]_{\frac{\pi}{4}}^{\frac{\pi}{2}}$
$A=[0-1]-[-\frac{1}{\sqrt 2}-\frac{1}{\sqrt 2}]$
$A=\sqrt 2-1$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 6 - Applications of the Integral - 6.1 Area Between Two Curves - Exercises - Page 286: 5
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