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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $ \int \limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \large\frac{\log (5 - \theta \sin \theta)}{\log (5+\theta \sin \theta)}$$d \theta$

\[\begin {array} {1 1} (a)\;0 \\ (b)\;1 \\ (c)\;2 \\ (d)\;None \end {array}\]

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A)
$\int \limits_{-a}^a f(x)dx =\int \limits_0^a f(x) =$ is even function
$f(x)=-f(-x)=0$
$f(-Q)=\int \limits_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \log \large\frac{ (5 +\theta \sin \theta)}{5-\theta \sin \theta}$
$f(Q)=-f(-Q)$
Then the solution will be zero.
Hence a is the correct answer.
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