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NewtonCotes Integration 
The NewtonCotes formulas, which have uniformly spaced grid points, are the most widely used numerical integration method. Common NewtonCotes formulas include: • Trapezoidal Rule (Linear) • Simpson's Rule (Parabolic) • Simpson's 3/8 Rule (Cubic) • Bode's Rule (4th degree polynomials) 
Gaussian Quadratures 
The Gaussian quadratures, which have nonuniformly spaced grid points, are very efficient for known smooth functions. Common Gaussian quadratures include: • GaussLegendre Formula for integration interval of . • GaussChebyshev Formula for integration interval of . • GaussHermite Formula for integration interval of . • GaussLaguerre Formula for integration interval of . 