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Formula(s) for composite/multiple-segment trapezoidal rule

  1. Jul 22, 2017 #1

    s3a

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    1. The problem statement, all variables and given/known data
    Hello, everyone. :)

    I'm looking at several different sources for the composite/multiple-segment trapezoidal rule (for approximating the value of an integral), but the formulas don't seem to agree.

    2. Relevant equations
    One place says I ≈ Δx/2 [f(a) + f(b)] + Δx Σ_(i=2)^(N-1) f(x_i).

    Another place says I ≈ Δx/2 [f(a) + f(b)] + Δx Σ_(i=2)^(N) f(x_i).

    Yet another place says I ≈ Δx/2 [f(a) + f(b) + 2 Σ_(i=1)^(N-1) f(a + iΔx)].

    3. The attempt at a solution
    Only the first one seems correct to me. Basically, the second one seems to me like it should end at N-1, not N, and the third one seems to me like it should end at N-2, not N-1.

    Am I right?
     
  2. jcsd
  3. Jul 22, 2017 #2

    scottdave

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    Homework Helper
    Gold Member

    You could set up a simple example, like if you are splitting your integral into 3 trapezoids. Then see how each of these formulas plays out in figuring it.
     
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