Question: Let x1, x2, ... , xn be distinct points in the interval [-1, 1] and let where the Li's are the Lagrange functions for the

Let x1, x2, ... , xn be distinct points in the interval [-1, 1] and let

where the Li's are the Lagrange functions for the points x1, x2, ... , xn.
(a) Explain why the quadrature formula

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 degree 0 polynomial and show that
A1 + A2 + ...... + An =2

.1 Ai= Li (x)dx, i=1 ,n f(x)dx = A1 f(xl ) + A2/(X2) + . . . + An f (x") -1

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