The value of $\int_\limits 0^{\pi /2} {\frac{{dx}}{{1 + {{\tan }^3}x}}}$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int\limits_{0}^{\pi /2} {\frac{{dx}}{{1 + {{\tan }^3}x}}}

View answer and explanation

Correct option: D

\frac{\pi}{4}

Option D (

\frac{\pi}{4}

) is correct because, by using the property of definite integrals and adding the original integral to the transformed one, the integral simplifies to

\frac{\pi}{4}

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