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 ?

Question

Let f be a real valued continuous function on 0 , &#160; 1 and f x = x + &#8747; 0 1 x - t f t d t . Then which of the following points x , &#160; y lies on the curve y = f x ?

Aicharya · Accepted Answer

Given, f x = x 1 + &#8747; 0 1 f t d t - &#8747; 0 1 t f t d t f x = A x - B &#160; . . . i A = 1 + &#8747; 0 1 f t d t = 1 + &#8747; 0 1 A t - B d t &#8658; A = 2 1 - B &#160; . . . i i Also B = &#8747; 0 1 t f t d t = &#8747; 0 1 A t 2 - B t d t A = 9 2 B &#160; . . . i i i From i i , &#160; i i i A = 18 13 , &#160; B = 4 13 So, f x = 18 13 x - 4 13 &#8658; f 6 = 18 &#215; 6 - 4 13 = 8

Let f be a real valued continuous function on 0 ,   1 and f x = x + ∫ 0 1 x - t f t d t . Then…

Solution

Let f be a real valued continuous function on 0 , &#160; 1 and f x = x + &#8747; 0 1 x - t f t d t . Then…

Solution

Let f be a real valued continuous function on 0 , 1 and f x = x + ∫ 0 1 x - t f t d t . Then…