Question

Integrate with respect to x:
${\sin }^{2}x$

Answer 1

$\Rightarrow \int {\sin }^{2}xdx$

$=\int \frac{1-\cos 2x}{2}dx$

$=\int \frac{1}{2}-\frac{\cos 2x}{2}dx$

$=\frac{1}{2}\times -\int \frac{\cos 2x}{2}dx$

$=\frac{1}{2}\times -\frac{1}{2}\int \cos 2xdx$

$=\frac{1}{2}\times -\frac{1}{2}\frac{1}{2}\int \cos tdt2x=t;2dx=dt;dx=dt/2$

$=\frac{1}{2}\times -\frac{1}{4}\sin t+C$

$\Rightarrow \frac{1}{2}\times -\frac{\sin 2x}{4}+C$