Problem 5. Matlab function Simpson given below implements Simpson’s 1/3 Rule to estimateI = So f(x)dx using n odd points.function I = Simpson (fun, a, b, n)% simpsonComposite Simpson’s rule%%% Synopsis: I = simpson (fun, a, b, npanel)% Input :fun= (string) name of the function that evaluates f (x)%a, b= lower and upper limits of the integraln= number of nodes, odd and > 2.% Output :I = approximate value of the integral from a to b of f(x)*dxif (mod (n, 2) == 0) || (n < 3)disp(' Warning: n must be > 1 and odd, program terminates . .. ‘) ;return;enddx = (b-a) / (n-1) ;% stepsizex = a: dx: b;divide the intervalf = feval (fun, x) ;% evaluate integrandI = (dx/3) *(f(1) + 4*sum(f (2:2:n-1) ) + 2*sum(f (3:2:n-2) ) + f(n));Now, it is desired to estimate the definite integral I1 =37 sin(x/3) da2 – cos(2/2)(6)correct to at least 4 significant digits, by the use of Simpson’s 1/3 rule. For this purpose start withn = 3 and increase n by 2 at a time until your result meets the required accuracy. Use Matlab functionSimpson given above for the solution of this problem. Compare your answer with Matlab’s quad ()function. Comment on your computation.
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