Let's consider a mid-point rectangular integration of a function $f(t)$ and suppose we are interested in:
$$\log\left(1 - \int_0^t f(z) \, dz\right) \approx \log \left(1 - \sum AUC_{\text{rect}_i} \right)$$
where $AUC_{\text{rect}_i}$ refers to the area under the $i^\text{th}$ rectangle. In my case, $f(z)$ involves power and $\exp()$ inside and sometimes becomes big. My question is whether there is anyway that I could bring log inside? So, I somehow get log of those $f(z)$ that are computationally managable?
Please let me know if you would need further explanation.
Thanks very much for your help and guidance