If $\mathop \smallint \limits_0^1 \,\,{\cot ^{ - 1}}\,\,\left( {1\,\, - \,\,x\,\, + \,\,{x^2}} \right)\,\,dx = k\,\mathop \smallint \limits_0^1 {\tan ^{ - 1}}\,\,x\,dx$, then $k = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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

, then

k =

View answer and explanation

Correct option: B

\mathrm{2}

Option B is correct because after applying properties of inverse trigonometric functions and simplifying,

k = 2

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