jee-advanced 2009 Q35

jee-advanced · India · paper2 Differential equations Integral Equations Reducible to DEs

Let $f:\mathbf{R}\rightarrow\mathbf{R}$ be a continuous function which satisfies $$f(x)=\int_{0}^{x}f(t)\,dt.$$ Then the value of $f(\ln5)$ is

Let $f:\mathbf{R}\rightarrow\mathbf{R}$ be a continuous function which satisfies
$$f(x)=\int_{0}^{x}f(t)\,dt.$$
Then the value of $f(\ln5)$ is