The correct option is A sin ^2 x ∫sin 2x dx =∫ 2sin xcos x dx Let t=sin x dt=cos x dx ⇒∫ 2tdt =t^2 +c =sin ^ 2x+c ...

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Theorems on Integration

Evaluate: ∫s...

Question

Evaluate:
$\int sin 2 x d x$

{sin}^{2} x

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{cos}^{2} x

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{tan}^{2} x

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None of the above

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Solution

The correct option is A ${sin}^{2} x$
$\int sin 2 x d x$

$= \int 2 sin x cos x d x$

Let $t = sin x ⟹ d t = cos x d x$

$\Rightarrow \int 2 t d t$

$= t^{2} + c$

$= {sin}^{2} x + c$

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