$\mathop \smallint \limits_{ - \pi /2}^{\pi /2} \,\,\frac{{\left| {\,x\,} \right|}}{{8\,\,{{\cos }^2}\,\,2x\,\, + \,\,1}}\,dx$ has the value

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \limits_{ - \pi /2}^{\pi /2} \,\,\frac{{\left| {\,x\,} \right|}}{{8\,\,{{\cos }^2}\,\,2x\,\, + \,\,1}}\,dx

has the value

View answer and explanation

Correct option: B

\frac{{{\pi ^2}}}{12}

Option B is correct because the integral is evaluated using properties of even functions and trigonometric substitutions.

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