Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 47

Answer

\[\frac{{\sqrt 2 }}{4}\]

Work Step by Step

\[\begin{gathered} \int_0^{\pi /8} {\cos 2x} dx \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ \frac{1}{2}\left[ {\sin 2x} \right]_0^{\pi /8} \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ = \frac{1}{2}\left[ {\sin 2\left( {\frac{\pi }{8}} \right) - \sin \left( 0 \right)} \right] \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ = \frac{1}{2}\left( {\frac{{\sqrt 2 }}{2}} \right) \hfill \\ \hfill \\ \frac{{\sqrt 2 }}{4} \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.