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I = 1-oa f(x) dx

I = 1-oa f(x) dx

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The exercise concerns the Gauss-Legendre integration method for integrals of the form that is in the picture i uploaded

with the difference that the integration will not be done at the N+1 specific points (or Gauss nodes: x_0, x_1, …, x_N) as tabulated in your book, but at N+1 points placed arbitrarily (but in monotonically increasing order) in the interval [-1, 1]. If f(x) is a polynomial of degree K, what is the largest value of K (expressed, obviously, as a function of N) for which the integral I is calculated exactly. Provide a convincing numerical demonstration of your answer for N=3 (choosing your own values for x_0, x_1, x_2, x_3).

I = 1-oa f(x) dx
Transcribed Image Text:I = 1-oa f(x) dx
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