The value of the integral $\mathop \smallint \limits_{ - \pi /2}^{\pi /2} \log \,\,\,\left( {\frac{{a\,\, - \,\,\sin \,\,\theta }}{{a\,\, + \,\,\sin \,\,\theta }}} \right)\,\,d\,\,\theta ,\,\,a > 0$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of the integral

\int \limits_{ - \pi /2}^{\pi /2} \log \,\,\,\left( {\frac{{a\,\, - \,\,\sin \,\,\theta }}{{a\,\, + \,\,\sin \,\,\theta }}} \right)\,\,d\,\,\theta ,\,\,a > 0

, is

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Correct option: A

\mathrm{0}

Option A (0) is correct because the integrand is an odd function, and the integral is evaluated over a symmetric interval.

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