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

MCQ

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

A
$\frac{x}{2}+\frac{\sin 2 x}{4}+C$
✓
$\frac{x}{2}-\frac{\sin 2 x}{4}+C$
C
$\frac{x}{2}+\frac{\cos 2 x}{4}+ C$
D
$\frac{x}{2}-\frac{\cos 2 x}{4}+C$

✓

Answer

Correct option: B.

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

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

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