The value of $\mathop \smallint \nolimits_{--{\rm{\pi }}/2}^{{\rm{\pi }}/2} \,\,\log \,\,\left( {\frac{{2\,\, - \,\,\sin \,\,\theta }}{{2\,\, + \,\,\sin \,\,\theta }}} \right)\,\,{\rm{d}}\theta \,\,is$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

\int \nolimits_{--\mathrm{\pi }/2}^{\mathrm{\pi }/2} \,\,\log \,\,\left( {\frac{{2\,\, - \,\,\sin \,\,\theta }}{{2\,\, + \,\,\sin \,\,\theta }}} \right)\,\,\mathrm{d}\theta \,\,is

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Correct option: A

\mathrm{0}

Option A (

\mathrm{0}

) is correct because the integrand is an odd function, and the integral is taken over a symmetric interval.

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