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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

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

, is

View answer and explanation

Correct option: B

\frac{\pi }{2}\,\, - \,\,\log \,\,2

Option B (

\frac{\pi }{2}\\ - \\,\log \\,2

) is correct because the integral is solved by using the property

\cot^{-1}(x) = \tan^{-1}(1/x)

and simplifying the integrand using the tangent addition formula.

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