Gaussian quadrature [6] ['Brute force' calculation of Gaussian quadrature weights and nodes]Letw₁f(x₁) +w₂f (x₂)(3)be a quadrature formula to approximate the integral ₁ f(x).Determine the weights {w₁, w2} and nodes {x₁, x2} such that (3) is exact(no error) for f(x) = 1, x, x², and x³. Then show that the formula is notexact for f(x) = x4 and conclude that the degree of exactness is N = 3.

Answered: Image /qna-images/answer/644dc99b-94c8-4974-96af-445bd3d4b2d8.jpg

[6] ['Brute force' calculation of Gaussian quadrature weights and nodes] Let (3) w₁ƒ(x1) +w2ƒ(x2) be a quadrature formula to approximate the integral ſ¹₁ ƒ(x). Determine the weights {w₁, w₂} and nodes {x₁, x2} such that (3) is exact (no error) for f(x) = 1, x, x², and x³. Then show that the formula is not exact for f(x) = x4 and conclude that the degree of exactness is N = 3. =

[6] ['Brute force' calculation of Gaussian quadrature weights and nodes] Let (3) w₁ƒ(x1) +w2ƒ(x2) be a quadrature formula to approximate the integral ſ¹₁ ƒ(x). Determine the weights {w₁, w₂} and nodes {x₁, x2} such that (3) is exact (no error) for f(x) = 1, x, x², and x³. Then show that the formula is not exact for f(x) = x4 and conclude that the degree of exactness is N = 3. =

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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