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Riemann Sum to integral

  1. Jun 9, 2010 #1
    If I have a function c(x,Δx) that gives the area between x and x + Δx of a function.
    The area under the function can be given by:
    Sum from j = 0 to n-1 of c(b/n j,c/b)
    As n tends to infinity and b is the upper limit of integration.

    How can I convert this from a sum into a integral? I'm not sure if this is already in the form of a Riemann integral or not.

    Thankyou in advance
     
  2. jcsd
  3. Jun 9, 2010 #2

    mathman

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    Please clarify this expression.
     
  4. Jun 10, 2010 #3
    Well c(x, Δx) is
    1/2 Csc(x) Csc(x + Δx) s(x) s(x + Δx) Sin(Δx)
    (Formula for the area of a triangle where Csc(x) s(x) are the length sides.

    Where s(x) is the solution for z of f(z) == z Cot(x).

    Where f(z) is the function I want to integrate. (I don't want to just integrate it f(z) dz)
     
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