$\mathop \smallint \nolimits_{ - \pi }^\pi \,\,\frac{{2x\,(1\,\, + \,\,\sin \,\,x)}}{{1\,\, + \,\,{{\cos }^2}\,\,x}}\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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\int \nolimits_{ - \pi }^\pi \,\,\frac{{2x\,(1\,\, + \,\,\sin \,\,x)}}{{1\,\, + \,\,{{\cos }^2}\,\,x}}\,\,dx

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Correct option: B

{\pi ^2}

Option B (

{\pi ^2}

) is correct because the integral simplifies to a solvable form using properties of definite integrals and trigonometric substitutions.

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