Answer Happy

f 9 dx 1. Evaluate the integral and compare the solution with the integral approximations 1 х using the midpoint rule, trapezoidal rule, and Simpson's rule with n=16 to determine the actual error with each estimate. After calculating the actual error with each integral approximation, use the error bound formulas for each integral approximation to calculate the associated error bound. Explain why the error bound either matches the actual error or differs from the actual error in each integral approximation. 2. Determine if there exists a continuous function f over a given interval (a,b) such that the actual error of the integral approximations using the trapezoidal rule, midpoint rule, and Simpson's rule satisfy the inequality |ET| < |EM| = |Esl. Justify your reasoning either with an example showing such a function exists along with the error calculations of each integral approximation method, or provide a proof demonstrating why no such function exists.