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

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

\[\begin {array} {1 1} (a)\;\pi \log \bigg(\frac{1}{2}\bigg) \\ (b)\;\log \bigg(\frac{1}{2}\bigg) \\ (c)\;3 \pi \log\bigg(\frac{1}{2}\bigg) \\ (d)\;None \end {array}\]

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1 Answer

$\int \limits_0^{\large\frac{\pi}{2}} \log (\sin x)^2 dx$
2$\int \limits_0^{\large\frac{\pi}{2}} \log \sin x dx$
=> $2. \large\frac{\pi}{2} $$. \log (1/2)$
=> $ \pi. \log (1/2) $
Hence a is the correct answer.
answered Dec 14, 2013 by meena.p
 
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