$\mathop \smallint \nolimits_0^{\pi /2} \,\,\frac{{{{\sin }^{2/3}}\,\,x}}{{{{\sin }^{2/3}}\,\,x\,\, + \,\,{{\cos }^{2/3}}\,\,x}}\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \nolimits_0^{\pi /2} \,\,\frac{{{{\sin }^{2/3}}\,\,x}}{{{{\sin }^{2/3}}\,\,x\,\, + \,\,{{\cos }^{2/3}}\,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{\mathrm{\pi }}{4}

Option A (

\frac{\mathrm{\pi }}{4}

) is correct because using the property of definite integrals,

\int_0^a f(x) dx = \int_0^a f(a-x) dx

, simplifies the integral.

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