MCQ
$\int \sin ^2 x d x$ का मान होगा$-$
  • 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.
$\frac{x}{2}-\frac{\sin 2 x}{4}+ C$
$\frac{x}{2}-\frac{\sin 2 x}{4}+ C$
$\int \sin ^2 x d x=\int\left(\frac{1-\cos 2 x}{2}\right) d x$
$\Rightarrow \quad \frac{1}{2} \int d x-\frac{1}{2} \int \cos 2 x d x$
$\Rightarrow \quad \frac{1}{2} x-\frac{1}{2} \frac{\sin 2 x}{2}+ C$
$\Rightarrow \quad=\frac{1}{2} x-\frac{1}{4} \sin 2 x+C$
अत: सही विकल्प $( B )$ है।

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