Problem 6: The formula -1 f(x)dx cof(-1)+c₁f(0) + c2f(1) is exact for all polynomials of degree less than or equal to 2. Determine co, c₁, and c2. Problem 7: Determine the value of n and h required to approximate 1 +4 dz to within 10-5 and compute the approximation using: a) Composite Trapezoid rule b) Composite Simpson's rule. Problem 8: Suppose that f(0) = 1, f(0.5)= 2.5, f(1) = 2, f(0.25) = f(0.75) = a, find a if the composite Trapezoid rule with n = 4 gives the value 1.75 for f(x)dr. Problem 9: Determine the degree of precision of the approximation 3h 31(0) f(x)dx = f(0)+3f(2h)]. Hint: Consider f(x) = 1, 2, 2, 3,..., etc. Problem 10: Use Gaussian quadrature with n = 3 to approximate fedr. Compare your results to the exact value of the integral and discuss the two. Problem 11: Determine constants a, b, c, d, and e that will produce a quadrature formula f(x)dx = af (-1)+bf (0) + cf(1) +dƒ'(−1)+ef'(1) that has degree of precision 4.