# RC Integrator mean value

i am trying to understand the behaviour of an RC integrator for $$\f>>1/RC\$$, i.e. in the integration domain. I know that at the capacitor i have $$\V = \int V_{in}/RC dt\$$; experimentally i find that when i use as input square waves with tunable duty cycle (but fixed frequency such that $$\f>>1/RC\$$) i have an approximate constant voltage at about the mean of the input signal (that obviously increases as the duty cycle increases).

I can't really understand why. I can approximate the integral with the mean, but then i have $$\ V= \bar{V_{in}} T/RC \$$ with T the period; this however tends to zero as T < RC!!

Thank you very much, i am using this to have a "tunable" voltage generator from Arduino, i know it works but i want to understand why it is working!