JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumIntegral Calculus369× since 2002If I=∫0π2sin12xsin2x+cos2x dxI = \int_0^{\frac{\pi}{2}} \frac{\sin \frac{1}{2} x}{\sin^2 x + \cos^2 x} \, dxI=∫02πsin2x+cos2xsin21xdx, then ∫02Ixsinxcosxsin2x+cos4x dx\int_0^{2I} \frac{x \sin x \cos x}{\sin^2 x + \cos^4 x} \, dx∫02Isin2x+cos4xxsinxcosxdx equals:AOption A. π212\frac{\pi^2}{12}12π2BOption B. π24\frac{\pi^2}{4}4π2COption C. π216\frac{\pi^2}{16}16π2DOption D. π28\frac{\pi^2}{8}8π2CheckStep-by-step hintSkip · show solution
