The value of $\mathop \smallint \limits_0^1 \,{\tan ^{ - 1}}\,\,\left( {\frac{{2x\,\, - \,\,1}}{{1 + \,\,x - \,\,{x^2}}}} \right)\,\,dx$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

\int \limits_0^1 \,{\tan ^{ - 1}}\,\,\left( {\frac{{2x\,\, - \,\,1}}{{1 + \,\,x - \,\,{x^2}}}} \right)\,\,dx

, is

View answer and explanation

Correct option: B

\mathrm{0}

Option B (0) is correct because the integral can be simplified using the property

\tan^{-1}(a) - \tan^{-1}(b) = \tan^{-1}(\frac{a-b}{1+ab})

and the substitution

x \rightarrow 1-x

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