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Simpson Rule equation's PROOF

  1. Jul 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Integral of f(x)dx from a to b~ S(n) = f(x0) + 4(x1) +2(x2) + 4(x3) + ...... 2(xn-2) + 4(xn-1) + f(xn))(Δx/3)

    You can use the formula for Simpson's Rule given above, but here is a better way. If you already have the Trapezoid Rule approximations T(2n) and T(n), the next Simpson's rule approximation follows immediately with a simple calculation

    S(2n) = (4T(2n) -T(n))/(3)

    Verify that for n=8, the two forms of the Simpson's Rule are the same.

    2. Relevant equations



    3. The attempt at a solution

    I tried to substitute a random function and attempt to go on from there but our professor said that we needed to solve this algebraically. Any help would be appreciated. Thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 3, 2013 #2

    LCKurtz

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    You have to show effort. What did you get for S(16) and (4T(16)-T(8))/3?

    Also you left out a bunch of f's in your formula for Simpson's rule.
     
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