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**limddavid** Question: "Determine constants a, b, c, d, e that will produce a quadrature formula

$\displaystyle \int_{-1}^{1}f(x)dx=af(-1)+bf(0)+cf(1)+df'(-1)+ef'(1)$

that has degree of precision 4"

Some background information: degree of precision of a quadrature formula is the largest positive integer n such that the formula is exact for x^k for each k = 0,1, ... , n.

I'm not sure about this problem... I think d and e are 0 because a quadrature formula is given by constants times certain values f(x) at different x's. ie. the quadrature formula is:

$\displaystyle \int_{a}^{b} f(x) dx \approx \sum_{i=0}^{n} a_{i} f(x_{i})$

Any suggestions?