Sorry, my wording was a bit unclear: what I meant was that they were probably taking the limit of \int_{0}^{r} s_{i} \* f_{i}(R - r)/r^2 + f_{i}'(R-r)/r w

Sorry, my wording was a bit unclear: what I meant was that they were probably taking the limit of \int_{0}^{r} s_{i} \* f_{i}(R - r)/r^2 + f_{i}'(R-r)/r with respect to some suitable sequence of functions `f_{i}` (narrower and narrower gaussians, for instance), for which `s` is actually well-defined.