Calculus: Early Transcendentals (2nd Edition)

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

Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises: 66

Answer

$$ - \cos 2\theta - \sin 4\theta + 2$$

Work Step by Step

$$\eqalign{ & f\left( \theta \right) = 2\sin 2\theta - 4\cos 4\theta \cr & {\text{find an antiderivative of }}f\left( \theta \right) \cr & F\left( \theta \right) = 2\left( { - \frac{1}{2}\cos 2\theta } \right) - 4\left( {\frac{1}{4}\sin 4\theta } \right) + C \cr & F\left( \theta \right) = - \cos 2\theta - \sin 4\theta + C \cr & {\text{using the initial condition }}F\left( {\frac{\pi }{4}} \right) = 2 \cr & 2 = - \cos 2\left( {\frac{\pi }{4}} \right) - \sin 4\left( {\frac{\pi }{4}} \right) + C \cr & 2 = - \cos \left( {\frac{\pi }{2}} \right) - \sin \left( \pi \right) + C \cr & 2 = - \left( 0 \right) - \left( 0 \right) + C \cr & C = 2 \cr & so, \cr & = - \cos 2\theta - \sin 4\theta + 2 \cr} $$
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.