(adsbygoogle = window.adsbygoogle || []).push({}); 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,x^{2}.

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. :)

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# Undetermined coefficients - deriving formula

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