1) If f(a+b−x)=f(x) then ∫baxf(x)dx is equal to A) a+b2∫baf(b−x)dx B) a+b2∫baf(b+x)dx C) b−a2∫baf(x)dx D) a+b2∫baf(x)dx Answer: Option DExplanation:Let I= ∫baxf(x)dx Let a+b-x= z ⇒ -dx=dz when x=a,z=b and when x=b,z=a ∴ I=−∫ab(a+b−z)f(z)dz I=(a+b)∫abf(x)dx−∫baxf(x)dx I=(a+b)∫abf(x)dx−I; 2I=(a+b)∫baf(x)dx Hence , I= (a+b2)∫baf(x)dx