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: 10

Answer

$$\sqrt 2 $$

Work Step by Step

$$\eqalign{ & \int_{ - \pi /4}^{\pi /4} {\cos xdx} \cr & {\text{ the function }}\cos x{\text{ is even}} \cr & {\text{Use the theorem 5}}{\text{.4}} \cr & {\text{If }}f\left( x \right){\text{ is even}}{\text{, }}\int_{ - a}^a {f\left( x \right)dx} = 2\int_0^a {f\left( x \right)dx} \cr & then \cr & = 2\int_0^{\pi /4} {\cos xdx} \cr & {\text{integrating}} \cr & = 2\left. {\left( {\sin x} \right)} \right|_0^{\pi /4} \cr & {\text{using the fundamental theorem}} \cr & = 2\left( {\sin \frac{\pi }{4} - \sin 0} \right) \cr & = 2\left( {\frac{{\sqrt 2 }}{2} - 0} \right) \cr & = \sqrt 2 \cr} $$
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