Q1: Li are the Lagrange basis functions given the interpolation points x0, x1,...xn.

How to know that the sum of Li(x) = 1?

Q2: For a Newton-Cotes rule , why does the sum of integration weights = b-a?

6. Prove that Coli(x) = 1 where l are the Lagrange basis functions given the interpolation points Co, X1, . . . , In. 7. Prove that for a Newton-Cotes rule fo f(x)dx ~ Eto wif(xi), the sum of integration weights E- Wi = b - a