If $I = \mathop \smallint \limits_0^1 \,\,\cos \,\,\left\{ {2{{\cot }^{ - 1}}\,\,\sqrt {\frac{{1 - x}}{{1 + x}}} } \right\}\,\,dx$ , then

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

I = \int \limits_0^1 \,\,\cos \,\,\left\{ {2{{\cot }^{ - 1}}\,\,\sqrt {\frac{{1 - x}}{{1 + x}}} } \right\}\,\,dx

, then

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Correct option: B

I = - \,\,\frac{1}{2}

Option C (

\pi

) is correct because the integral of the odd functions over the symmetric interval is zero, and only the integral of 1 remains.

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