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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $ \int \sin ^3 x .dx$

\[\begin {array} {1 1} (a)\;\frac{3}{4}\sin x -\frac{1}{12} \sin 3x +c\\ (b)\;\frac{-3}{4} \cos x +\frac{1}{12} \cos 3x +c \\ (c)\;\frac{3}{4}\cos x +\frac{1}{12} \cos 3x +c \\ (d)\;None \end {array}\]

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A)
$\sin 3x.dx= 3 \sin x -4 \sin ^3 x $
$\sin ^3 x =\large\frac{3 \sin x - \sin 3x}{4}$
=> $\int \large\frac{3}{4}$$ \sin x - \frac{1}{4} \sin 3x dx$
=> $\large\frac{-3}{4}$$ \cos x +\large\frac{1}{12}$$ \cos 3x +c$
Hence b is the correct answer.
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