The value of $\mathop \smallint \nolimits_0^{\pi /2} \,\,\frac{{{{\sin }^2}\,\,x\,\, - \,\,{{\cos }^2}\,\,x}}{{{{\sin }^3}\,\,x\,\, + \,\,{{\cos }^3}\,\,x}}\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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The value of

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

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Correct option: A

\mathrm{0}

Option A is correct because the integral evaluates to 0 due to the symmetry and properties of definite integrals.

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