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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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$I= \int \sin ^3 x \sin 2x dx$ Find the value of I

\[\begin {array} {1 1} (a)\;\frac{1}{5} \\ (b)\;\frac{2}{5} \\ (c)\;\frac{3}{5} \\ (d)\;0 \end {array}\]
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1 Answer

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$\int \limits_0^{\frac{\pi}{2}} \sin ^3 x \sin 2x dx$
$\qquad= \int \limits_0^{\frac{\pi}{2}} 2 \sin ^4 x \cos x dx$
$\sin x =t$
$\cos x dx=dt$
$\int \limits _0^1 2 t^4 dt$
$\qquad= \large\frac{2t^5}{5} \bigg]_0^1 $
$\qquad=\large\frac {2}{5}$
Hence b is the correct answer.
answered Dec 20, 2013 by meena.p
 
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