Question

∫f(t) x∈[0,x] dt = x + ∫t f(t) x ∈[x,1] dt, then f(1) is equal to

(a)  1/2

(b)   0

(c)   1

(d)  -1/2

Answer 1

Correct option (a) 1/2

Explanation:

Differentiate both sides w.r.t x

⇒ f(x) = 1 + (0 - xf(x)) ⇒f(x) = 1/1 + x

f(1) = 1/2