function disk_integrands_test01 ( )

%*****************************************************************************80
%
%% disk_integrands_test01: integral of X^E in the unit disk.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    19 April 2019
%
%  Author:
%
%    John Burkardt
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'disk_integrands_test01\n' );
  fprintf ( 1, '  Use a simple Monte Carlo approach to estimate the\n' );
  fprintf ( 1, '  integral of X^E over the circle of radius 1\n' );
  fprintf ( 1, '  centered at the origin.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '           N   E       Exact Approximate   Error\n' );

  for e = 2 : 2 : 6
    fprintf ( 1, '\n' );
    p01_param_set ( e );
    n = 1;
    for n_log2 = 0 : 20
      seed = 123456789;
      [ xy, seed ] = disk_unit_sample ( n, seed );
      f = p01_f ( n, xy );
      q = disk_unit_area ( ) * sum ( f ) / n;
      t = p01_exact ( );
      fprintf ( 1, '  %10d  %2d  %10.4f  %10.4f  %10.4e\n', n, e, t, q, abs ( t - q ) );
      n = n * 2;
    end
  end

  return
end
