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Q)

The value of $ \int\limits_{0}^{\pi}\sin^{2}x\cos^{3}x dx$ is

\[\begin{array}{1 1}(1)\pi&(2)\pi/2\\(3)\pi/4&(4)0\end{array}\]

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A)
$f(x)=\sin^2 x \cos ^3 dx$
$f( \pi -x)=[\sin (\pi -x)^2][cos (\pi -x)]$
$\qquad= \sin ^2 [-\cos x]^3$
$\qquad= \sin^2 x\; x - \cos ^3 x$
$\qquad= -\sin^2 x \cos ^3 x$
$\qquad= -f(x)$
$ \int\limits_{0}^{\pi}\sin^{2}x\cos^{3}x dx=0$
Hence 4 is the correct answer.
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