JEE Advance - Mathematics (1985 - No. 37)
Evaluate the following : $$\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx$$
$$\frac{\pi^2}{32}$$
$$\frac{\pi^2}{8}$$
$$\frac{\pi^2}{4}$$
$$\frac{\pi^2}{16}$$
$$\frac{\pi^2}{64}$$