We have to fond the integral of sin x cos x
Solution
To find the \(\int \sin x\cos x\)
We will use the given trigonometric identity
We know the identity
\(\sin 2x= 2\sin x \cos x\)Substituting the identity in the given integral we get
\(\int \sin x\cos x=\frac{1}{2}\int \sin 2x\)Let u = 2x and du=2dx
\(\int \sin x\cos x=\frac{1}{4}\int \sin u . du\) \(\int \sin x\cos x=-\frac{1}{4}\cos u + C\)Answer
\(\int \sin x\cos x=-\frac{1}{4}\cos u + C\)
