The Newton-Cotes formulas, which have uniformly spaced grid points, are the most widely used numerical integration method. Common Newton-Cotes formulas include:

• Trapezoidal Rule (Linear)

• Simpson's Rule (Parabolic)

• Simpson's 3/8 Rule (Cubic)

• Bode's Rule (4th degree polynomials)

The Gaussian quadratures, which have non-uniformly spaced grid points, are very efficient for known smooth functions. Common Gaussian quadratures include:

• Gauss-Legendre Formula for integration interval of .

• Gauss-Chebyshev Formula for integration interval of .

• Gauss-Hermite Formula for integration interval of .

• Gauss-Laguerre Formula for integration interval of .