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Elementary Numerical Analysis : Gaussian Numerical Integration

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1. Show that if an integration formula of the form

In ( f ) = ∑ wjf(xj)

is exact when integrating 1, x, x2, ..., xm, then it is exact for all polynomials of degree ≤ m.

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A proof involving Gaussian numerical integration is provided. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.

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1. Show that if an integration formula of the form

In ( f ) = ∑ ...

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