Let f be a real valued continuous function on 0 , 1 and f x = x + ∫ 0 1 x - t f t d t . Then which of the following points x , y lies on the curve y = f x ?

Step-by-step solution

Given, f x = x 1 + ∫ 0 1 f t d t - ∫ 0 1 t f t d t f x = A x - B   . . . i A = 1 + ∫ 0 1 f t d t = 1 + ∫ 0 1 A t - B d t ⇒ A = 2 1 - B   . . . i i Also B = ∫ 0 1 t f t d t = ∫ 0 1 A t 2 - B t d t A = 9 2 B   . . . i i i From i i ,   i i i A = 18 13 ,   B = 4 13 So, f x = 18 13 x - 4 13 ⇒ f 6 = 18 × 6 - 4 13 = 8