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

also,

f’(x) = f(x), x > 0

⇒ f(x) = k, x > 0

Since, f(0) = 0 and f(x) is continuous,

so f(x) = 0 ∀ x > 0

Therefore, f(ln 5) = 0