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Connection between summation and integration

  1. Dec 30, 2013 #1

    I want you note this similarity:
    [tex]\\ \int xdx=\frac{1}{2}x^2+C \\ \int x^2dx=\frac{1}{3}x^3+C[/tex]
    [tex]\\ \sum x\Delta x=\frac{1}{2}x^2-\frac{1}{2}x+C \\ \\ \sum x^2\Delta x=\frac{1}{3}x^3-\frac{1}{2}x^2+\frac{1}{6}x+C[/tex]

    Seems there be a connection between the discrete calculus and the continuous. Exist some formula that make this connection? Given the summation of a function f(x) is possible to know the integral of f(x), or, given the integral of a function f(x) is possible know the summation of f(x)?
  2. jcsd
  3. Dec 30, 2013 #2


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    Science Advisor

    This is studied in time scales calculus, a very active field of research today. It's only been around for thirty or so years
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