Thread: plz help me with SIMPSON rule in Matlab

1. plz help me with SIMPSON rule in Matlab

Hi guys, i got a simpson's rule code, but i dont know how to use it.

Code:
function [integral,difference,ratio]=simpson(a,b,n0,index_f)
%
%  function [integral,difference,ratio]=simpson(a,b,n0,index_f)
%
%  This uses Simpson's rule with n subdivisions to integrate the function
%  f over the interval [a,b].  The values of n used are
%        n = n0,2*n0,4*n0,...,256*n0
%  The value of n0 MUST be nonzero.
%  The corresponding numerical integrals are returned in the vector
%  integral.  The differences of successive numerical integrals are
%  returned in the vector difference:
%        difference(i) = integral(i)-integral(i-1),  i=2,...,9
%  The entries in ratio give the rate of decrease in these
%  differences.
%
%  In using this program, define the integrand using the
%  function given below.  The parameter index_f allows the user
%  to do calculations with multiple integrands.
% Initialize output vectors.
integral = zeros(9,1);
difference = zeros(9,1);
ratio = zeros(9,1);
% Initialize for Simpson integration.
sumend = f(a,index_f) + f(b,index_f);
sumodd = 0;
sumeven = 0;
% Initialize for case of n0 > 2.
if(n0 > 2)
h = (b-a)/n0;
for i=2:2:n0-2
sumeven = sumeven + f(a+i*h,index_f);
end
end
%  Calculate the numerical integrals, doing each
%  by appropriately modifying the preceding case.
for i=1:9
n = (n0)*(2^(i-1));
h = (b-a)/n;
sumeven = sumeven + sumodd;
sumodd = 0;
for k=1:2:n-1
sumodd = sumodd + f(a+k*h,index_f);
end
integral(i) = h*(sumend + 4*sumodd + 2*sumeven)/3;
end
%  Calculate the differences of the successive
%  Simpson rule integrals and the ratio
%  of decrease in these differences.
difference(2:9)=integral(2:9)-integral(1:8);
ratio(3:9)=difference(2:8)./difference(3:9);

function f_value = f(x,index)
%
% This defines the integrand.
switch index
case 1
f_value = exp(-x.^20;
case 2
f_value=1./(1+x.^2)
case 3
f_value=1./(2+cos(x));

end

IF I want to use it to integrate f(x)= x.^(1/2) * exp(x) , how can i write in the command window?

Thx

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