(a) Write a Matlab function that compute the numerical integral using the composite Boole's rule with...

 

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(a) Write a Matlab function that compute the numerical integral using the composite Boole's rule with the definition where function numI = compBoole (f, a, b, N) a, f b : N : num I returned numerical integral. : function to be integrated, left and right end points of the interval, number of intervals, (b) Use your function compBoole.m to compute the integral of f(x) = e-x/2 on the interval [-3, 3] with N uniform intervals. Take number of intervals N to be 5 * 2k, with k = 1,2,3,4,5, The exact integral is 27 erf (32/2), where erf is a matlab built-in function. Print out the number of divided intervals along with the absolute numerical error. Plot the error against the divided interval length (b-a)/N = 6/N using loglog scale. Numerically compute the rate of convergence for this rule. You shall observe the rate is approximately 6. (a) Write a Matlab function that compute the numerical integral using the composite Boole's rule with the definition where function numI = compBoole (f, a, b, N) a, f b : N : num I returned numerical integral. : function to be integrated, left and right end points of the interval, number of intervals, (b) Use your function compBoole.m to compute the integral of f(x) = e-x/2 on the interval [-3, 3] with N uniform intervals. Take number of intervals N to be 5 * 2k, with k = 1,2,3,4,5, The exact integral is 27 erf (32/2), where erf is a matlab built-in function. Print out the number of divided intervals along with the absolute numerical error. Plot the error against the divided interval length (b-a)/N = 6/N using loglog scale. Numerically compute the rate of convergence for this rule. You shall observe the rate is approximately 6.