How do you integrate sin(x)cos(x)?

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

\(\int \sin x\cos x=-\frac{1}{4}\cos u + C\)

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