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

Integrate : $ \int \sqrt{\sin ^3 x}. \cos x \;dx$

\[\begin {array} {1 1} (a)\;\frac{2}{5} (\cos x)^{5/2}+c \\ (b)\;\frac{2}{5}(\sin x)^{5/2}+c \\ (c)\;\frac{2}{3}(\tan x)^{3/2} \\ (d)\;None \end {array}\]

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A)
$\sin x =t=> \cos x dx =dt$
$ \int (t)^{\large\frac{3}{2}}$$.dt$
$\large\frac{2}{5}$$ t^{5/2} +c$
$\large\frac{2}{5}$$(\sin x)^{5/2}+c$
Hence b is the correct answer.
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