Question

Find the integration of $\sin x\cos xdx$.

Answer 1

Find the integration of the given function

Given function: $\sin x\cos x$

Let $u=\sin x$

By differentiating the both sides we get,

$du=\cos xdx$
Now, by substituting these values in $\int \sin x\cos xdx$, we get,

$\int \sin x\cos xdx=\int udu$

$=\frac{u^2}{2}+C$, where $C$is the integration constant.

$=\frac{{\sin }^{2}x}{2}+C\left[\because u=sinx\right]$
Hence, the integration of $\sin x\cos xdx$ is$\frac{{\sin }^{2}x}{2}+C$, where $C$is the integration constant.