JEE Advance - Mathematics (1991 - No. 23)
Evaluate $$\,\int\limits_0^\pi {{{x\,\sin \,2x\,\sin \left( {{\pi \over 2}\cos x} \right)} \over {2x - \pi }}dx} $$
This integral requires advanced techniques and the answer is not directly obtainable.
The integral evaluates to 8/π²
The integrand has a singularity at x = π/2, requiring special attention.
The solution involves trigonometric identities and careful simplification.
The integral diverges.