function [T, t, y] = trapezoid(f, a, b, n)
% TRAPEZOID   Trapezoid formula for numerical integration.
%
% Input:
%   f     integrand (function, must accept vector argument)
%   a,b   interval of integration (scalars)
%   n     number of interval divisions
%
% Output:
%   T     approximation to the integral of f over (a,b)
%   t     vector of nodes used
%   y     vector of function values at nodes
%
    h = (b - a)/n;
    t = a + h*(0:n)';
    y = f(t);
    T = h * ( sum(y(2:n)) + 0.5*(y(1) + y(n+1)) ); 
end