function xSingularInt
% 奇異函數的積分例子
% An Example of Integration of a Singular function f(x) from a to b
% by using 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;
b = 1;
d = pi/50; 
t = a:d:b;
y = func(t);

format long

% 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)

% ------------------------------------------------------------------
function y = func(t)      % 奇異函數(Singular function)
y = 1./(t.^(1/2)+t.^(1/3));