Answer
$$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{x}{1+\cos ^{2}x}dx=0$$
Work Step by Step
$$let\ f(x)=\frac{x}{1+\cos ^{2}x}$$
$$f(-x)=\frac{-x}{1+\cos ^{2}x}=-f(x)$$
$$so, f(x)\ is\ odd$$
$$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f(x)dx=0$$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises - Page 508: 35
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