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Relationship between Riemann Sum and the Integral

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data

    The notation for a Riemann sum - Ʃ f(x*i)Δx - is very similar to the notation for the integral (the Ʃ becomes ∫, the f(x*i) becomes f(x) and the Δx becomes dx).

    [tex]\int f(x)dx = \lim_{n \to \infty}\sum_{k=0}^{n} f(x_i) Δx[/tex]

    Is there a way to explicitly define the values on the right hand side in terms of the left hand variables (for instance to define dx in terms of Δx)? Or is it just that the whole left side equals the right side and that's it?

    Thank you.
     
    Last edited: Nov 4, 2012
  2. jcsd
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