For the preceding problem, write a script-m file to do the following: a. Calculate the integral using the trapezoidal rule with 1, 2, 4, 8, 16, 32, 64, 128, and 256 subdivisions of the integration domain, in sequence. You may use the available function-m file for the trapezoidal rule. b. Print the results for the nine cases. c. Richardson extrapolation gives S h T h T h ( ) ( ) ( ) = 4 2 − 3 where T(h) is the integral from the trapezoidal rule for step size h and T(2h) that for step size 2h and S is the result from Simpson’s rule. Using this equation and results from Part a, calculate the Simpson’s rule results for the different subdivisions considered. d. Print the results obtained. e. From the results, how many subdivisions are satisfactory for the trapezoidal and Simpson’s rules?
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