Question

Let f: R → R be a continuous function which satisfies f(x) = ∫f(t) dt for t ∈ [0,x]. Then the value of f(ln 5) is ... 

Answer 1

Given,

f'(x) = f(x)

When x = 0, y = 0, then A = 0 

Thus, y = Ae^x = 0 

f(x) = 0 

f(ln5) = 0