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I have a set of data, call it x

_{i}(ρ), which I want to integrate over some distribution function (log-normal in this case) given by f(ρ). In particular I want to compute the integral

∫ x(ρ) ρ f(ρ) dρ

from 0 to infinity (although since I don't have x

_{i}(ρ) from 0 to infinity I'd cut the calculation off at some upper and lower bound where f(ρ) becomes negligible).

So I have a functional form for ρ f(ρ), but only have values for x(ρ) at discrete values of ρ. How can I do this integral accurately in Mathematica?