$\mathop \smallint \nolimits_{\pi /6}^{\pi /3} \,\,\frac{{dx}}{{1 + \sqrt {\tan \,\,x} }}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\int \nolimits_{\pi /6}^{\pi /3} \,\,\frac{{dx}}{{1 + \sqrt {\tan \,\,x} }}

is equal to

View answer and explanation

Correct option: A

\frac{\pi }{{12}}

Option A (

\frac{\pi }{{12}}

) is correct because using the property of definite integrals

\int \nolimits_a^b f(x) dx = \int \nolimits_a^b f(a + b - x) dx

simplifies the integral to

\frac{\pi}{12}

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