Let x1, x2, . . . , xn be distinct points in the interval [1, 1] and let Ai = _ 1 1 Li
Chapter 5, Problem 15(choose chapter or problem)
Let x1, x2, . . . , xn be distinct points in the interval [1, 1] and let Ai = _ 1 1 Li (x)dx, i = 1, . . . , n where the Li s are the Lagrange functions for the points x1, x2, . . . , xn. (a) Explain why the quadrature formula _ 1 1 f (x)dx = A1 f (x1)+ + An f (xn) will yield the exact value of the integral whenever f (x) is a polynomial of degree less than n. (b) Apply the quadrature formula to a polynomial of degree 0 and show that A1 + A2 + + An = 2 1
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