Problem 1. Consider evaluating the following integral 0 f(x) Use MATLAB to numerically integrate f (x) using a) The trapezoidal rule to find T,(/) for all n E (2,4,8,16,32,64. b) Simpson's rule to find S,() for all n E (2,4,8,16,32,64) and c) Estimate the asymptotic errors E, (f) and E-l(f), for the trapezoidal rule and Simpson's rule, and compute the estimated asymptotic error ratios to see if you get error ratio 4 for the trapezoidal rule and 16 for Simpson's rule