Consider evaluating the following integral I(f)=3x-4xdx f(x) Use MATLAB to numerically integrate f(x) using and a)...

 

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Consider evaluating the following integral I(f)=3x-4xdx f(x) Use MATLAB to numerically integrate f(x) using and a) The trapezoidal rule to find T(f) for all ne {2,4,8,16,32,64}. b) Simpson's rule to find S, (f) for all n = {2,4,8,16,32,64}. c) Estimate the asymptotic errors , (f) and ,(f), for the trapezoidal rule and Simpson's rule, and compute the estimated asymptotic error ratios E(f) P = (S) to see if you get error ratio 4 for the trapezoidal rule and 16 for Simpson's rule. Consider evaluating the following integral I(f)=3x-4xdx f(x) Use MATLAB to numerically integrate f(x) using and a) The trapezoidal rule to find T(f) for all ne {2,4,8,16,32,64}. b) Simpson's rule to find S, (f) for all n = {2,4,8,16,32,64}. c) Estimate the asymptotic errors , (f) and ,(f), for the trapezoidal rule and Simpson's rule, and compute the estimated asymptotic error ratios E(f) P = (S) to see if you get error ratio 4 for the trapezoidal rule and 16 for Simpson's rule.