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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \nolimits_0^{\mathrm{\pi }/2} \,\,\frac{{{{\sin }^2}\,\,x}}{{{{\sin }^2}x\,\, + \,\,{{\cos }^2}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 the integral is solved using the property of definite integrals and symmetry.

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