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

Integrate : $ \int \limits_0^{\large\frac{\pi}{2}} min ^m \{ \tan x , \cot x \} dx$

\[\begin {array} {1 1} (a)\;\log \sqrt 2 \\ (b)\;\log 2 \sqrt 2 \\ (c)\;\log(\frac{1}{2}) \\ (d)\;\log 2 \end {array}\]
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1 Answer

To solve this type are throw graph. to $min ^m$, take lower portion.
=> $\int \limits_0^{\large\frac{\pi}{4}}$$ \tan x dx + \int \limits ^{\large\frac{\pi}{2}}_{\frac{\pi}{4}} \cot x dx$
=>$ \bigg[\log |\sec x|\bigg]_0^{\large\frac{\pi}{4}}+ \bigg[ \log |\sin x| \bigg]_{\frac{\pi}{4}}^{\frac{\pi}{2}}$
=> $\log | \sec \large\frac{\pi}{4}|$$ - | \sec 0| + \log | \sin \large\frac{z}{2}|$$ - \log \sin \large\frac{\pi}{2}$
=> $ \log \sqrt 2 -\log (1) + \log |1| - \log | \large\frac{1}{\sqrt 2}|$
=> $2 \log \sqrt 2$
=> $\log (\sqrt (2)^2)$
=> $ \log_e^2$
answered Dec 13, 2013 by meena.p
edited Oct 9, 2014 by sharmaaparna1
 

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