Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 408: 2



Work Step by Step

Verify $\int\cos^2{x}dx=\frac{1}{2}x+\frac{1}{4}\sin{2x}+C$ We need to take the derivative of the right side of our equation and verify that it equals the expression inside of our integral. \begin{equation*} \frac{d}{dx}\left(\frac{1}{2}x+\frac{1}{4}\sin{2x}+C\right)=\frac{d}{dx}\left(\frac{1}{2}x\right)+\frac{d}{dx}\left(\frac{1}{4}\sin{2x}\right)+\frac{d}{dx}\left(C\right) \end{equation*} \begin{equation*} =\left(\frac{1}{2}\right)+\left(\frac{1}{4}\cos{2x}\times2\right)+\left(0\right) \end{equation*} \begin{equation*} =\frac{1}{2}+\frac{1}{2}\cos{2x}=\frac{1+\cos{2x}}{2}=\cos^2{x} \end{equation*} Hence the result is verified.
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.