I often see people use the Riemann definition of the integral to solve a certain limit-series computation, but they usually just skip a step that I can follow one way but not the other. Given the integral, I can see the limit-series that comes from it, but when trying to find the integral from the limit-series I have a problem.(adsbygoogle = window.adsbygoogle || []).push({});

For example, over the interval a=0 and b=1, [tex]\int^1_0 f(x) dx = \lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^{n} f\left(\frac{k}{n}\right)[/tex] using Riemann Upper sums.

So basically If required to somehow work out [tex]f(k/n) = something[/tex], so that I can re-express it in terms of f(x). So i guess the question is, does anyone know a general method to spot the function of k/n, as to find f(x) ?

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# Using Riemann Upper sums to solve limits

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