Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Connection between summation and integration

  1. Dec 30, 2013 #1
    Hellow!

    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

    pwsnafu

    User Avatar
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Connection between summation and integration
Loading...