JEE Main 2003Annual, Paper 1MathematicsMediumIntegral Calculus369× since 2002If f(a+b−x)=f(x)f\left( {a + b - x} \right) = f\left( x \right)f(a+b−x)=f(x) then ∫abxf(x)dx\int\limits_a^b {xf\left( x \right)dx}a∫bxf(x)dx is equal toAOption A. a+b2∫abf(a+b+x)dx{{a + b} \over 2}\int\limits_a^b {f\left( {a + b + x} \right)dx}2a+ba∫bf(a+b+x)dxBOption B. a+b2∫abf(b−x)dx{{a + b} \over 2}\int\limits_a^b {f\left( {b - x} \right)dx}2a+ba∫bf(b−x)dxCOption C. a+b2∫abf(x)dx{{a + b} \over 2}\int\limits_a^b {f\left( x \right)dx}2a+ba∫bf(x)dxDOption D. b−a2∫abf(x)dx\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx}2b−aa∫bf(x)dxCheckSkip · show solution
