function y=besintJ0(x)
%-----------------------------------------------------------------------
% Approximate the Bessel's function of the first kind of order zero
% via the following integral definition.
%   J0(x) = (1/pi)*integral (from 0 to pi) of cos(x*sin(q))*dq
% Programming Note:
%   For large values of x, apply the asymptotic approximation formula.
%     J0(x)=sqrt(2/pi/x)*cos(x-pi/4),  for x>25
% Instructor: Nam Sun Wang
%-----------------------------------------------------------------------

      global xx
%     pi = 3.141593  already defined in Matlab

% Pass x into the integrand through "common"
      xx = x;

% Call an integration routine to do the grunt work.
%     y = 1/pi * quad8('bintegra', 0, pi);  ... old
      y = 1/pi * quadl('bintegra', 0, pi);