## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 24

#### Answer

$$\frac{1}{4} \cos^4(2- x) +c$$

#### Work Step by Step

Given $$\int \cos ^{3} (2-x) \sin (2-x) d x$$ Let $$u=\cos(2-x)\ \ \ \Rightarrow \ \ du =\sin (2-x)dx$$ Then \begin{align*} \int \cos ^{3} (2-x) \sin (2-x) d x&=\int u^{3} d u\\ &= \frac{1}{4}u^4 +c\\ &= \frac{1}{4} \cos^4(2- x) +c \end{align*}

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.