Let's say I have some differential $dy/dt$. I want to calculate the definite integral over some interval $t = 0-T$ i.e.
$$ y(T) = \int_0^{T} \frac{dy}{dt} dt$$
My question is if $dy/dt$ is very small such that $dy/dt << T$ is there some approximation scheme (perturbative or otherwise) that I can use for calculating $y(T)$?
Thanks in advance
Some extra background:
I have an equation for $dy/dt$ that I have lifted from a paper that described the evolution of some quantity over time. I could integrate this numerically, but I would also like an analytical expression. $dy/dt$ is very small and I want to integrate for a time $T$ which is very large.
It doesn't seem likely that any good estimation system should exist. The fact that $\frac {dy}{dt}$ is very small probably only means we have a bound |$\frac {dy}{dt}$| < k for some constant k. This would only practically give an upper bound |y(t)|< kT, which would be quite useless since T is quite large.