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Undetermined coefficients - deriving formula

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Derive a formula of the form [tex]\int\stackrel{b}{a}f(x)dx \approx c_{0}f(a)+c_{1}f(b)+c_{2}f'(a)+c_{3}f'(b)[/tex] that is exact for polynomials of the highest degree possible.

    Apply a change of variable: y=x-a

    2. Relevant equations



    3. The attempt at a solution
    I don't get the "highest degree possible" thing. Like, if it's exact for quadratics, I know it has to be exact for f(x)=1,x,x2.

    But applying the change of variable, I got [tex]\int\stackrel{b-a}{0}f(y)dy \approx c_{0}f(0)+c_{1}f(b-a)+c_{2}f'(0)+c_{3}f'(b-a)[/tex]

    Any help much appreciated. :)
     
    Last edited: Apr 26, 2010
  2. jcsd
  3. Apr 26, 2010 #2
    Whoops, that's meant to be integral from a to b for the first one and 0 to b-a for the second one.
     
  4. Apr 26, 2010 #3
    Can anyone even point me in the right direction?
     
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