Question: Approximate f(1) by using Newton's interpolating polynomial corresponding to the data I -2-102 f(x) 0 -424 Consider the integral I = xdx. a) Derive

Approximate f(1) by using Newton's interpolating polynomial corresponding to the data I -2-102 f(x) 0 -424 Consider the integral I = xdx. a) Derive two-point Gaussian quadrature. (f(x)dr Auf (ro) + Aif(ri)). Use monomials (1,1,2,3). Approximate the integral I by using the two-point Gaussian quadrature. b) Approximate the integral I by using the Simpson's 1/3 rule with 11 points.

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