Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.4 Working with Integrals - 5.4 Exercises: 1

Answer

If $f$ is an odd function, $\int_{-a}^{a} f(x) dx = 0$ because of symmetry. Exactly one half of the total area will be negative and another half will be positive, making the net area zero.

Work Step by Step

$\int_{-a}^{a} f(x) dx = \int_{-a}^0 f(x) dx + \int_0^a f(x) dx = -n + n = 0$, where $n$ is the value given when evaluating the integral.
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