Exercise 1 Consider the following integral of a function f(r) on a finite interval [a, Write three Matlab/Octave functions implementing, respectively, the composite midpoint rule, the composite trapezoidal rule, and the composite Simpson rule to compute the numerical approxima- tion of I(f). Such functions should be of the form function [I]-intmidpoint.rule(fun,a,b,n)(composite midpoint rule) function [Il-int.trapezoidal.rule(fun,a,b,n) (composite trapezoidal rule) function [1]=int.Simpson-rule (fun , a,b,n) (composite Simpson rule) Input fun: function handle representing f(x) a, b: endpoints of the integr n: number of evenly-spaced points m [a, ation interval (including endpoints) Output: I: numerical approximation of the integral (1) Exercise 2 Use the functions you coded in Exercise 1 to compute the numerical approximation of the integral To this end, write a Matlab/Octave function [en,et ,es] function test-integration() that returns the following items: . en, ot, es: row vectors with components the absolute values of the integration errors |ref-1.1 Inl2,3. 10000 n=2.3. 1 obtained with the midpont (vector en). trapezoidal (vector et) and Simpson (vector es) rules. Here Iref = 1.6851344770476 is the reference value of the integral (2) while In is the nucal approximation obtained by using the composite midpoint, trapezoidal, and Simpson rules with nnodes The function test.integrationO should also return the plot of the integrand function ap- pearing in (2 in figure(1), and the plots of the errors en, et and es versus n in a log-log scale in figure (2) (one figure with three plots). (Hint:us the Matlab command loglog))