The value of the integral $\mathop \smallint \limits_{ - \pi /3}^{\pi /3} \,\,\frac{{x\,\,\sin \,\,x}}{{{{\cos }^2}\,\,x}}\,\,dx$, is

$\left( {\pi /3\,\, - \,\,\log \,\,\tan \,\,3\pi /2} \right)$

$3\,\,\left( {\pi /2\,\, - \,\,\log \,\,\sin \,\,\pi /12} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

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

, is

View answer and explanation

Correct option: B

2\,\,\left( {2\pi /3\,\, - \,\,\log \,\,\tan \,\,5\pi /12} \right)

Option B (

2\,\left( {2\pi /3\, - \,\log \,\tan \,5\pi /12} \right)

) is correct because it is the result of evaluating the definite integral using integration by parts and properties of even functions.

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