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13-May-2025 16:52:59
quad_monte_carlo_test():
  MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7
  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 =       0.3661149362346841

  Estimate integral ( 0.0 < x < 2.0 ) sqrt(x) dx
  quad_monte_carlo: n = 1000, integral estimate q =        1.864765610737556

  Estimate integral ( 0.0 < x < 2.0 ) humps(x) dx
  quad_monte_carlo: n = 1, integral estimate q =       -6.620446448091433
  quad_monte_carlo: n = 2, integral estimate q =        4.949749444936288
  quad_monte_carlo: n = 4, integral estimate q =       0.8163777562460686
  quad_monte_carlo: n = 8, integral estimate q =        18.71704042764326
  quad_monte_carlo: n = 16, integral estimate q =        49.40001761039119
  quad_monte_carlo: n = 32, integral estimate q =        28.83145397274741
  quad_monte_carlo: n = 64, integral estimate q =         26.0172784655622
  quad_monte_carlo: n = 128, integral estimate q =        19.78716691143935
  quad_monte_carlo: n = 256, integral estimate q =        32.65448495217483
  quad_monte_carlo: n = 512, integral estimate q =        26.80145919801749
  quad_monte_carlo: n = 1024, integral estimate q =        27.53238278852324
  quad_monte_carlo: n = 2048, integral estimate q =        28.87684144749323
  quad_monte_carlo: n = 4096, integral estimate q =        29.77098650155325
  quad_monte_carlo: n = 8192, integral estimate q =        28.76128249946415
  quad_monte_carlo: n = 16384, integral estimate q =        29.43056509410382
  quad_monte_carlo: n = 32768, integral estimate q =         29.5861781074986
  quad_monte_carlo: n = 65536, integral estimate q =        29.19892111386281
  quad_monte_carlo: n = 131072, integral estimate q =        29.23190133151778
  quad_monte_carlo: n = 262144, integral estimate q =        29.28579187437449
  quad_monte_carlo: n = 524288, integral estimate q =        29.29021917550511
  quad_monte_carlo: n = 1048576, integral estimate q =        29.29415594327526

quad_monte_carlo_test():
  Normal end of execution.
13-May-2025 16:52:59