function integral = trapezoidal_integration (fhandle, a, b, num_segments)

%TRAPEZOIDAL_INTEGRATION  Computes a definite integral
%   INTEGRAL = TRAPEZOIDAL_INTEGRATION ( FHANDLE, A, B, NUM_SEGMENTS )
%   determines the integral of the function defined by FHANDLE between the
%   bounds of A and B. The integration interval [A,B] is divided into
%   NUM_SEGMENTS segments of equal width and the multiple application
%   trapezoidal integration rule is applied.
%
%   Inputs:
%      FHANDLE:   a Matlab function handle for the function to be
%                 integrated.
%      A:         Lower bound of the integration interval
%      B:         Upper bound of the integration interval
%      NUM_SEGMENTS: the number of segments into which the interval is
%                 divided to approximate the integral
%
%   Outputs:
%      INTEGRAL:  The result of the integration.
%
%   Assumptions:
%      - The function is continuous and smooth.
%      - the function pointed to by FHANDLE supports vector operations
%
%% ME 2016 Section
%% Fall 2007
%%
%% AUTHOR:  Chris Paredis
%%

% error checking
% make sure the number of segments is a whole number larger than 0
num_segments = round(num_segments);
if num_segments<1
    error('the number of segments must be larger than or equal to 1');
end

% compute the function values.
% Note: the number of function values is num_segments+1
x_values = linspace(a,b,num_segments+1);
f_values = fhandle(x_values);  % make sure to use vector operations here!
h = (b-a)/num_segments; % segment width

% use the multiple application rule
integral = h * (sum(f_values(2:end-1)) + 0.5*(f_values(1)+f_values(end)));