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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $ \int \limits _0^{n \pi +v} |\cos x | dx $

\[\begin {array} {1 1} (a)\;\sin v -2n \\ (b)\;\sin v +2n-1 \\ (c)\;\sin v+2n \\ (d)\;1+2n- \cos v \end {array}\]

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1 Answer

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$\int \limits_0^v |\cos x| dx + \int \limits_{v+0}^{n \pi +v} |\cos x| dx \qquad 0 < v < \large\frac{z}{2} $
$\int \limits_0^v (cos x) dx + \int \limits_{v+0}^{nz} |\cos x| dx$
$\int \limits_0^v (cos x) dx + n \int \limits_0^z |\cos x| dx$
$\int \limits_0^v cos x dx + n \int \limits_0^{\pi/2} (\cos x) dx- n \int \limits _{\pi/2} ^{\pi} \cos x dx $
=> $| \sin ]_0^v + n [ (\sin x )_0^{\pi/2} -(\sin x )_{\pi/2}^\pi]$
=> $\sin v -\sin 0 + n [1-0-0+1]$
=>$\sin v +2n$
Hence c is the correct answer.
answered Dec 14, 2013 by meena.p
 
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