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The value of $\int\limits_{0}^{\pi}\sin^{4}x dx$ is

\[\begin{array}{1 1}(1)3\pi/16&(2)3/16\\(3)0&(4)3\pi/8\end{array}\]

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1 Answer

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$\sin ^4(\pi-x)=\sin ^4 x$
$\int \limits_0^{\pi} \sin ^4 x.dx=2 \int _0^{\pi/2} \sin ^4 x.dx $
$\qquad= 2. \large\frac{4-1}{4} .\frac{4-3}{2} .\frac{\pi}{2}$
$\qquad= 2 \times \large\frac{3}{4} \times \frac{1}{2} \times \frac{\pi}{2}$
$\qquad= \large\frac{3 \pi}{8}$
Hence 4 is the correct answer.
answered May 21, 2014 by meena.p
 
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