Develop an M-file function to implement Romberg integration based on Fig. 20.2. Test the function by using it to determine the integral of the polynomial from Example 20.1. Then use it to solve Prob. 20.1.

Fig.20.2

Example 20.1

Data From Problem 20.1

Use Romberg integration to evaluate

to an accuracy of ε_s = 0.5%.Your results should be presented in the format of Fig. 20.1. Use the analytical solution of the integral to determine the percent relative error of the result obtained with Romberg integration. Check that ε_t is less than ε_s.

function [q, ea, iter] =romberg (func, a, b, es, maxit, varargin) romberg: Romberg integration quadrature q = romberg (func, a, b, es, maxit, p1, p2, ...): Romberg integration. 8 f & input: 8 func = name of function to be integrated a, b = integration limits 8 es = desired relative error (default = 0.000001%) & maxit = maximum allowable iterations (default = 30) 8 & pl, p2, ... = additional parameters used by func & output: q= integral estimate 8 8 ea = approximate relative error (8) iter = number of iterations if nargin