$\mathop \smallint \nolimits_{ - \pi /3}^{\pi /3} \,\,\frac{{x\,\,\sin \,\,x}}{{{{\cos }^2}\,\,x}}\,\,dx$ is equal to

$\frac{1}{3}\,\,\left( {4\pi + 1} \right)$

$\frac{{4\pi }}{3}\,\, + \,\,\log \,\,\tan \,\,\frac{{5\pi }}{{12}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\int \nolimits_{ - \pi /3}^{\pi /3} \,\,\frac{{x\,\,\sin \,\,x}}{{{{\cos }^2}\,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: B

\frac{{4\pi }}{3}\,\, - \,\,2\,\,\log \,\,\tan \,\,\frac{{5\pi }}{{12}}

Option B (

\frac{{4\pi }}{3}\, - \,2\,\log \,\tan \,\frac{{5\pi }}{{12}}

) is correct because after applying integration by parts and simplifying, the result matches this option.

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