Exercise "Monte Carlo integration"

1. Implement plain Monte Carlo multi-dimensional integration.
2. Calculate ∫₀^π  dx/_π ∫₀^π  dy/_π ∫₀^π  dz/_π [1-cos(x)cos(y)cos(z)]^-1 = Γ(1/4)⁴/(4π³) ≈  1.3932039296856768591842462603255
3. Calculate some interesting integrals with your Monte-Carlo routine.

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4. If you are using C/C++, compare your implementation with the GSL's gsl_monte_plain_integrate and gsl_monte_vegas_integrate.
5. If there exists a Monte Carlo package for your language, compare it with your implementation.

Projects

1. Stratified sampling.
2. Quasi-random sampling.