💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

JH

# Evaluate $\displaystyle \int \sin x \cos x dx$ by four methods:(a) the substitution $u = \cos x$ (b) the substitution $u = \sin x$ (c) the identity $\sin 2x = 2 \sin x \cos x$ (d) integration by partsExplain the different appearances of the answers.

## a) $$-\frac{1}{2} \cos ^{2} x+C$$b) $$\frac{1}{2} \sin ^{2} x+C$$c) $$-\frac{1}{4} \cos 2 x+C$$d) $$-\frac{1}{2} \cos ^{2} x+C, \quad\left(\text { also } \frac{1}{2} \sin ^{2} x+C \text { if you used } u=\sin x\right)$$

#### Topics

Integration Techniques

### Discussion

You must be signed in to discuss.
##### Top Calculus 2 / BC Educators  ##### Catherine R.

Missouri State University  ##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp

### Video Transcript

JH

#### Topics

Integration Techniques

##### Top Calculus 2 / BC Educators  ##### Catherine R.

Missouri State University  ##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp