Find the value of ^2 x d x : - Vidyadip

Question

Find the value of $\int \sin ^2 x\ d x$ :

✓

Answer

$\int \sin ^2 x d x=\int\left(\frac{1-\cos 2 x}{2}\right) d x$
$\Rightarrow \frac{1}{2} \int d x-\frac{1}{2} \int \cos 2 x\ d x$
$\Rightarrow \frac{1}{2} x-\frac{1}{2} \frac{\sin 2 x}{2}+C$
$=\frac{1}{2} x-\frac{1}{4} \sin 2 x+C$
Hence option $(B)$ is correct.

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