The value of $\mathop \smallint \nolimits_0^{{\rm{\pi }}/2} \,\,\frac{{\cos \,\,{\rm{\theta }}}}{{\sqrt {4\,\, - \,\,{{\sin }^2}\,\,{\rm{\theta }}} }}\,\,d{\rm{\theta }}$ is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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The value of

\int \nolimits_0^{\mathrm{\pi }/2} \,\,\frac{{\cos \,\,\mathrm{\theta }}}{{\sqrt {4\,\, - \,\,{{\sin }^2}\,\,\mathrm{\theta }} }}\,\,d\mathrm{\theta }

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Correct option: B

\frac{\mathrm{\pi }}{6}

Option B (

\frac{\mathrm{\pi }}{6}

) is correct because after substitution, the integral becomes a standard arcsin integral, evaluating to

\frac{\pi}{6}