15-May-2025 20:28:34
quad_monte_carlo_test():
  MATLAB/Octave version 6.4.0
  quad_monte_carlo() is an interactive program which uses
  n random samples to estimate the integral of a
  function f(x) over the interval [a,b].

  Estimate integral ( 0.000000 < x < 1.000000 ) x.^2 dx
  quad_monte_carlo: n = 100, integral estimate q =       0.3510828062054355

  Estimate integral ( 0.0 < x < 2.0 ) sqrt(x) dx
  quad_monte_carlo: n = 1000, integral estimate q =        1.894589278159285

  Estimate integral ( 0.0 < x < 2.0 ) humps(x) dx
  quad_monte_carlo: n = 1, integral estimate q =        -3.37956310170822
  quad_monte_carlo: n = 2, integral estimate q =        67.98446867164319
  quad_monte_carlo: n = 4, integral estimate q =        3.269107169642018
  quad_monte_carlo: n = 8, integral estimate q =        11.43135586243907
  quad_monte_carlo: n = 16, integral estimate q =        48.24612882673249
  quad_monte_carlo: n = 32, integral estimate q =        17.80507122704366
  quad_monte_carlo: n = 64, integral estimate q =         35.4061981006837
  quad_monte_carlo: n = 128, integral estimate q =        31.30634748655782
  quad_monte_carlo: n = 256, integral estimate q =        26.91667592384626
  quad_monte_carlo: n = 512, integral estimate q =        30.66669408230868
  quad_monte_carlo: n = 1024, integral estimate q =        30.46601495925954
  quad_monte_carlo: n = 2048, integral estimate q =        31.35068271350133
  quad_monte_carlo: n = 4096, integral estimate q =        29.24733063316754
  quad_monte_carlo: n = 8192, integral estimate q =        29.48656460856864
  quad_monte_carlo: n = 16384, integral estimate q =        29.28407639878871
  quad_monte_carlo: n = 32768, integral estimate q =         29.2548019381295
  quad_monte_carlo: n = 65536, integral estimate q =        29.51444238423417
  quad_monte_carlo: n = 131072, integral estimate q =        29.26295950089641
  quad_monte_carlo: n = 262144, integral estimate q =        29.51759074400325
  quad_monte_carlo: n = 524288, integral estimate q =        29.32218025986039
  quad_monte_carlo: n = 1048576, integral estimate q =        29.40499736131865

quad_monte_carlo_test():
  Normal end of execution.
15-May-2025 20:28:34