Question: Prove the statement following Definition 4.1; that is, show that a quadrature formula has degree of precision n if and only if the error E(P(x))

Prove the statement following Definition 4.1; that is, show that a quadrature formula has degree of precision n if and only if the error E(P(x)) = 0 for all polynomials P(x) of degree k = 0, 1, . . . , n, but E(P(x)) ≠ 0 for some polynomial P(x) of degree n + 1.

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