#### Answer

$A=\sqrt 2-1$

#### Work Step by Step

$A=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(sin(x)-cos(x))dx$
$A=[-cos(x)-sin(x)]_{\frac{\pi}{4}}^{\frac{\pi}{2}}$
$A=[0-1]-[-\frac{1}{\sqrt 2}-\frac{1}{\sqrt 2}]$
$A=\sqrt 2-1$

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Published by
W. H. Freeman

ISBN 10:
1464125260

ISBN 13:
978-1-46412-526-3

$A=\sqrt 2-1$

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