$\mathop \smallint \limits_0^{\pi /2} \,\,\left( {x\,\,\sqrt {\tan \,\,x} \,\, + \,\,\sqrt {\cot \,\,x} } \right)\,\,dx$ equals

$\frac{{{\pi ^2}}}{{2\,\sqrt 3 }}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \limits_0^{\pi /2} \,\,\left( {x\,\,\sqrt {\tan \,\,x} \,\, + \,\,\sqrt {\cot \,\,x} } \right)\,\,dx

equals

View answer and explanation

Correct option: C

\frac{{{\pi ^2}}}{{2\,\,\sqrt 2 }}

Option C (

\frac{{{\pi ^2}}}{{2\sqrt 2 }}

) is correct because it is the result of evaluating the definite integral using properties of definite integrals and trigonometric substitutions.

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