I have some function $f(x)$, which I'd like to integrate to find, $F(r) = \int_r^\infty f(x) dx $. Is there a way to do this using the values parametrized in log-space? I.e. some function $G(r, \log[F(x)], \log x) = F(r)$?
For numerical reasons, I only have the two arrays, $X_i = \log x_i$, and $Y_i = \log[ f(x_i) ]$. Obviously, converting to $f_i$ and $x_i$ would be possible, but would introduce significant numerical issues.