s=simprl(f,a,b,M)

function s=simprl(f,a,b,M)

%Input     - f is the integrand 
%             - a and b are upper and lower limits of integration
%             - M is the number of subintervals
%Output  - s is the simpson rule sum

%If f is defined as an M-file function use the @ notation
% call s=simprl(@f,a,b,M).
%If f is defined as an anonymous function use the
% call s=simprl(f,a,b,M).

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

h=(b-a)/(2*M);
s1=0;
s2=0;

for k=1:M
   x=a+h*(2*k-1);
   s1=s1+f(x);
end
for k=1:(M-1)
   x=a+h*2*k;
   s2=s2+f(x);
end

s=h*(f(a)+f(b)+4*s1+2*s2)/3;