Quadrature

Riemann sums, Simpson’s rule, Gauss-Legendre, Euler-Maclaurin, Romberg, Clenshaw-Curtis, tanh-sinh, and QUADPACK-style adaptive quadrature.

Gaussian quadrature: optimal nodes are exact to degree 2n-1

Gaussian quadrature: optimal nodes are exact to degree 2n-1

Simpson’s rule: parabolas through pairs of panels

Simpson's rule: parabolas through pairs of panels

Riemann sums: the definition of the integral

Riemann sums: the definition of the integral

Euler-Maclaurin: correcting the trapezoidal rule

Euler-Maclaurin: correcting the trapezoidal rule

Romberg integration: extrapolating the trapezoidal rule

Romberg integration: extrapolating the trapezoidal rule

Clenshaw-Curtis vs. Gauss-Legendre quadrature

Clenshaw-Curtis vs. Gauss-Legendre quadrature

Tanh-sinh quadrature: integrating endpoint singularities

Tanh-sinh quadrature: integrating endpoint singularities

Adaptive quadrature (QUADPACK): subdividing where it is needed

Adaptive quadrature (QUADPACK): subdividing where it is needed