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I want to evaluate " sum f(x) g'(x)" the limits of sum goes from 0---> infinity.

I know how to solve this problem using integration by substitution method. I also know that using Riemann sum we can convert summation into integration, but I am still curious whether the Riemann sum can be used to convert summation problem (as given above) into its equivalent integration by substitution ?

Regards, uzma

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So you mean $\sum_{x=0}^\infty f(x)g'(x)$ ? I don't think you can simply write that as an integral, though you can test it for convergence using the integral test. –  ljfa Mar 5 '14 at 6:51

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