function xIntegration
% 積分例子
% An Example of Integration of a function f(x) from a to b
% by using TRAPZ (trapezoidal numerical integration),
% QUAD (adaptive Simpson quadrature), and  QUADL (adaptive Lobatto quadrature)
%
%   Author: HUANG Huajiang
%   Copyright 2002 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2002/05/9 $

clear all
clc

% the interval: [a, b], the step: d
a = 0;          % 積分下限
b = 3*pi;       % 積分上限
d = pi/1000;    % 積分步長 
t = a:d:b;
y = func(t);

format long 

% 梯形數值積分(Trapezoidal numerical integration)
y_trapz = trapz(y) * d  

% 自適應Simpson法(Adaptive Simpson quadrature, low order) 
y_quad = quad(@func,a,b)

% 自適應Lobatto求積法(Adaptive Lobatto quadrature, high order)
y_quadl = quadl(@func,a,b)

disp('Results:')
disp('   Trapz              Qquad              Quadl')
disp([y_trapz,y_quad,y_quadl])

% ------------------------------------------------------------------
function y = func(t)  
y = exp(-0.5*t) .* sin(t+pi/6);