$ti(t)$ is a function of time which is normally given with (time,value) pairs and not defined mathematically. i need to get the value $td(t)$ by solving the following integration:
$$\int_{t-td(t)}^t\frac{1}{ti(\tau)}d\tau==1$$
so how can I get the values of $td(t)$?
I know that $\int\frac{1}{x}dx = \ln(x)$. Yet, I am not sure how to do it when I only have a numerical values of function $ti(t)$.
Can anyone help me?
thx for the support
Of course only a numerical solution is available.
To compute the integral you can use, for example, http://en.wikipedia.org/wiki/Trapezoidal_rule. You only need to know the values of the function $ti(t)$ in some points. (the more the better).
Once you've done that, it should not be too difficult to find the solution to your problem.
You can use, for example, http://en.wikipedia.org/wiki/Bisection_method.