# Numerical integration

 Calculator name Summary Trapezoid, Midpoint and Simpson integrationsTrapezoid, Midpoint and Simpson integrations Calculate a table of the integrals of the given function f(x) over the interval (a,b) using Trapezoid, Midpoint and Simpson's methods. Tanh-Sinh integration (a,b)Tanh-Sinh integration (a,b) Calculates the integral of the given function f(x) over the interval (a,b) using Tanh-Sinh method (Double exponential formula). Tanh-Sinh integration_2 (a,b)Tanh-Sinh integration_2 (a,b) Calculates a table of the successive integral estimates of the given function f(x) over the interval (a,b) by increasing partitions from n to n+9 using Tanh-Sinh method. Tanh-Sinh integration_3 (a,b)Tanh-Sinh integration_3 (a,b) Calculates a table of the successive integral estimates of the given function f(x) over the interval (a,b) by doubling partitions from two to N using the Tanh-Sinh method. Double exponential integration (a,∞)Double exponential integration (a,∞) Calculates the integral of the given function f(x) over the semi-infinite interval (a,∞) using the Double exponential formula. Double exponential integration (-∞,b)Double exponential integration (-∞,b) Calculates the integral of the given function f(x) over the semi-infinite interval (-∞,b) using the Double exponential formula. Double exponential integration (-∞,∞)Double exponential integration (-∞,∞) Calculates the integral of the given function f(x) over the infinite interval (-∞,∞) using the Double exponential formula. Gaussian quadratureGaussian quadrature Calculates the integral of the given function f(x) over the interval (a,b) using Gaussian quadrature. (i.e. Gauss-Legendre, Gauss-Chebyshev 1st, Gauss-Chebyshev 2nd, Gauss-Laguerre, Gauss-Hermite, Gauss-Jacobi, Gauss-Lobatto and Gauss-Kronrod) Gauss-Legendre integrationGauss-Legendre integration Calculates the integral of the given function f(x) over the interval (a,b) using Gauss-Legendre integration. Gauss-Kronrod integrationGauss-Kronrod integration Calculates the integral of the given function f(x) over the interval (a,b) using Gauss-Kronrod integration. Gauss-Lobatto integrationGauss-Lobatto integration Calculates the integral of the given function f(x) over the interval (a,b) using Gauss-Lobatto integration. Gauss-Chebyshev integrationGauss-Chebyshev integration Calculates the integral of the given function f(x) over the interval (a,b) using Gauss-Chebyshev integration. Gauss-Laguerre integrationGauss-Laguerre integration Calculates the integral of the given function f(x) over the interval (0,∞) using Gauss-Laguerre integration. Gauss-Hermite integrationGauss-Hermite integration Calculates the integral of the given function f(x) over the interval (-∞,∞) using Gauss-Hermite integration. Romberg integrationRomberg integration Calculates the integral of the given function f(x) over the interval (a,b) using the Romberg Method. Romberg arrayRomberg array Calculates the Romberg array produced by applying Richardson’s extrapolation procedure, which forms the basis of the Romberg Method. Nodes and Weights of Tanh-SinhNodes and Weights of Tanh-Sinh Calculates the nodes and weights of the Tanh-Sinh integration. Nodes and Weights of Gaussian quadratureNodes and Weights of Gaussian quadrature Calculates the nodes and weights of the Gaussian quadrature. (i.e. Gauss-Legendre, Gauss-Chebyshev 1st, Gauss-Chebyshev 2nd, Gauss-Laguerre, Gauss-Hermite, Gauss-Jacobi, Gauss-Lobatto and Gauss-Kronrod) Nodes and Weights of Gauss-LegendreNodes and Weights of Gauss-Legendre Calculates the nodes and weights of the Gauss-Legendre integration. Nodes and Weights of Gauss-KronrodNodes and Weights of Gauss-Kronrod Calculates the nodes and weights of the Gauss-Kronrod integration. Nodes and Weights of Gauss-BondNodes and Weights of Gauss-Bond Calculates the nodes and weights of the Gauss-Bond integration. Nodes and Weights of Gauss-LobattoNodes and Weights of Gauss-Lobatto Calculates the nodes and weights of the Gauss-Lobatto integration. Nodes and Weights of Gauss-ChebyshevNodes and Weights of Gauss-Chebyshev Calculates the nodes and weights of the Gauss-Chebyshev integration. Nodes and Weights of Gauss-LaguerreNodes and Weights of Gauss-Laguerre Calculates the nodes and weights of the Gauss-Laguerre integration. Nodes and Weights of Gauss-HermiteNodes and Weights of Gauss-Hermite Calculates the nodes and weights of the Gauss-Hermite integration.