If ∫₀^π xf(sin x)dx = A∫₀^(π /2) f(sin x)dx, then A is

Integral Calculus: JEE Main 2004 Mathematics question

JEE Main 2004 · Annual, Paper 1 · Q3335

JEE Main 2004Annual, Paper 1MathematicsEasyIntegral Calculus369× since 2002

\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} }

then

A

JEE Main 2004 · Annual, Paper 1 · Q3335

JEE Main 2004Annual, Paper 1MathematicsEasyIntegral Calculus369× since 2002

\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} }

then

A