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(10%) (Numerical Integration) Consider a numerical integration rule dened as: A new a Ame) + Am) + Asia), (4) where A1, A2, and A3 are the weights. R3 of 5 (a) (6%) Find the values of A], A2, and A3 such that the numerical integra- tion rule (4) is exact for all f(:r:) 6 H2, i.e., the set of all polynomials with degree at most 2; (b) (4%) What is the order of accuracy of the numerical integration rule (4) with the weights A], A2, and A3 obtained in part (a)