So, rephrasing what I found so far, also thanks to discussing in the comments, I think it might help to write a new answer to myself, as I need to put also some graphics in it.
My problem is that I have a theoretical capacitance, and naturally it loses potential as long as the energy is taken from it. This capacitance is used to power some devices, which in the end are not important, it just matters that such devices are taking a known amount of constant current for a known period of time. The capacitor has a known initial voltage, and it is known the minimum allowable voltage we need.
The energy the capacitor can provide, is $$ E_{c} = \frac{1}{2} C (V_{init}^2 - V_{final}^2) $$.
The energy the devices are using can be found through the usage time and their current, but the voltage is dropping. So is NOT possible to assume $$ E_{used} = (V_{init} - V_{final}) I_{active} t $$, because I am interested in finding the total energy used to make such drop in C, not just it's delta:
[![enter image description here][1]][1]
So in order to find the energy the devices are using (is the first area in the graph), I must simply do some geometry:
$$ E = P_{min} t_{max} + \frac{(P_{max} - P_{min}) t_{max}}{2} $$
And finally I can compare this to the original energy the capacitor can provide to see if the circuit will stay within specifications.
Any thoughts? [1]: https://i.sstatic.net/hFTDa.png
