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JEE Advance - Mathematics (1996 - No. 1)

For $$n>0,$$ $$\int_0^{2\pi } {{{x{{\sin }^{2n}}x} \over {{{\sin }^{2n}}x + {{\cos }^{2n}}x}}} dx = $$
$\frac{\pi}{2}$
$\pi$
$\pi^2$
$2\pi$
$\frac{\pi^2}{4}$

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