Answer
$\frac{\pi}{2}$
Work Step by Step
See figure. The enclosed area can be written as
$\int_{-\pi/4}^{\pi/4} (sec^2x-tan^2x) dx =\int_{-\pi/4}^{\pi/4} (1) dx=x|_{-\pi/4}^{\pi/4} =\frac{\pi}{4}-(-\frac{\pi}{4})=\frac{\pi}{2} $
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 5: Integrals - Section 5.6 - Definite Integral Substitutions and the Area Between Curves - Exercises 5.6 - Page 304: 67
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