Let f: R → R be a continuous function which satisfies f(x) = ∫₀ˣ f(t)dt. Then the value of f(ln5) is?

f(x) = ∫₀ˣ f(t)dt
Substitute x = 0, then integral of f(t) from 0 to 0 will become 0.
⇒ f(0) = 0
Now, differentiate both side of given integral
f'(x) = f(x), x > 0
⇒ f(x) = keˣ, x > 0
∵ f(0) = 0 and f(x) is continuous
⇒ f(x) = 0, x > 0
∴ f(ln5) = 0