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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $ \int \sqrt {1+ \sin 4x}$$dx$

$(a)\;\frac{\cos 2x}{2} -\frac{\sin 2x}{2}+c \qquad(b)\;\frac{-\cos x}{2}+\frac{\sin x}{2}+c \qquad(c)\;\frac{\cos x}{2}-\frac{\sin x}{2}+c \qquad (d)\;\frac{-\cos 2x}{2}+\frac{\sin 2x}{2}+c $
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1 Answer

$\int \sqrt { \sin ^2 2x +\cos ^2 2x + 2 \sin 2x \cos 2 x }dx$
$\sin ^2 \alpha + \cos ^2 \alpha=1$
$\sin 2 \alpha = 2 \sin \alpha \cos \alpha$
$\int \sqrt { (\sin 2x+ \cos 2x)^2}$$dx$
$\int (\sin 2x+ \cos 2x) dx$
$ \large\frac{-\cos 2x}{2}+\frac{\sin 2x}{2}$$+c $
Hence d is the correct answer.
answered Dec 24, 2013 by meena.p
 
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