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

Integrate:$\int \limits_0^{\large\frac{\pi}{2}} \sin x \sin 2x \;dx$

\[\begin {array} {1 1} (a)\;\frac{4}{3} \\ (b)\;\frac{1}{3} \\ (c)\;\frac{3}{4} \\ (d)\;\frac{2}{3} \end {array}\]

1 Answer

$\int \limits_0^{\large\frac{\pi}{2}} 2 \sin ^2 x \cos x \;dx$
$\sin x=t, \qquad t=0=> x=0$
$\cos x dx=dt, \qquad t=1=> x=\large\frac{z}{2}$
$\int \limits_0^1 2. t^2.dt$
=> $\large\frac{2}{3} $$\bigg[t^3\bigg]_0^1$
=> $\frac{2}{3}$
Hence d is the correct answer.

 

answered Dec 17, 2013 by meena.p
 
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