JEE Main 2006Annual, Paper 1MathematicsEasyIntegral Calculus369× since 2002∫0πxf(sinx)dx\int\limits_0^\pi {xf\left( {\sin x} \right)dx}0∫πxf(sinx)dx is equal toAOption A. π∫0πf(cosx)dx\pi \int\limits_0^\pi {f\left( {\cos x} \right)dx}π0∫πf(cosx)dxBOption B. π∫0πf(sinx)dx\,\pi \int\limits_0^\pi {f\left( {sinx} \right)dx}π0∫πf(sinx)dxCOption C. π2∫0π/2f(sinx)dx{\pi \over 2}\int\limits_0^{\pi /2} {f\left( {sinx} \right)dx}2π0∫π/2f(sinx)dxDOption D. π∫0π/2f(cosx)dx\pi \int\limits_0^{\pi /2} {f\left( {\cos x} \right)dx}π0∫π/2f(cosx)dxCheckSkip · show solution
