Numerical Integration
 Numerical Integration
 Numerical Methods Linear Algebra Root Finding Interpolation Integration Newton-Cotes Formulas Gaussian Quadratures ODE Resources Bibliography

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 For indefinite integral formulas, click here. Newton-Cotes Integration 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)
 Gaussian Quadratures 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 .