T=rctrap(f,a,b,n)

function T=rctrap(f,a,b,n)

%Input  - f is the integrand input as a string 'f'
%       - a and b are upper and lower limits of integration
%       - n is the number of times for recursion
%Output - T is the recursive trapezoidal rule list

% NUMERICAL METHODS: MATLAB Programs
%(c) 1999 by John H. Mathews and Kurtis D. Fink
%To accompany the textbook:
%NUMERICAL METHODS Using MATLAB,
%by John H. Mathews and Kurtis D. Fink
%ISBN 0-13-270042-5, (c) 1999
%PRENTICE HALL, INC.
%Upper Saddle River, NJ 07458

M=1;
h=b-a;
T=zeros(1,n+1);
T(1)=h*(feval(f,a)+feval(f,b))/2;

for j=1:n
   M=2*M;
   h=h/2;
   s=0;
   for k=1:M/2
      x=a+h*(2*k-1);
      s=s+feval(f,x);
   end
   T(j+1)=T(j)/2+h*s;
end