numerical integration algorithm details

[yangyongkang]

The numerical integration algorithm is introduced in the Wolfram reference documentation.

* NIntegrate uses symbolic preprocessing to resolve function symmetries, expand piecewise functions into cases, and decompose regions specified by inequalities into cells.
*With Method->Automatic, NIntegrate uses "GaussKronrod" in one dimension, and "MultiDimensional" otherwise.
*If an explicit setting for MaxPoints is given, NIntegrate by default uses Method->"QuasiMonteCarlo".
*"GaussKronrod": adaptive Gaussian quadrature with error estimation based on evaluation at Kronrod points.
*"DoubleExponential": non-adaptive double-exponential quadrature.
*"Trapezoidal": elementary trapezoidal method.
*"Oscillatory": transformation to handle certain integrals containing trigonometric and Bessel functions.
*"MultiDimensional": adaptive Genz\[Dash]Malik algorithm.
*"MonteCarlo": non-adaptive Monte Carlo.
*"QuasiMonteCarlo": non-adaptive Halton\[Dash]Hammersley\[Dash]Wozniakowski algorithm.