a) Compute In = " x2 sin(x) dx for n = 2, 4, 10, 20, 50, and 100 using Newton-Cotes quadrature. b) Compute the error, en = I - I,, for each n, given that the exact solution to the definite integral is I = 12 - 4Problem 27 Estimate the value of dx (x4+ 2)1/2 Using (a) Midpoint (1-point) Gauss quadrature (b) 2-point Gauss quadrature (c) 3-point Gauss quadrature Two point Gauss quadrature points and weights: 1 1 {x1, x2) = (-73'13' and {w1, w2) = {1, 1}. Three point Gauss quadrature points and weights: 5 8 5 {x1, *2, x3) = {- ,0, and {w1, w2, wa] = (9'9'9)