quadrature formulas

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a, b], divide it into n equal parts such that f_n = f(x_n) and h congruent (b - a)/n. Then find polynomials which approximate the tabulated function, and integrate them to approximate the area under the curve. To find the fitting polynomials, use Lagrange interpolating polynomials. The resulting formulas are called Newton-Cotes formulas, or quadrature formulas.

Boole's rule | difference equation | Durand's rule | finite difference | Gaussian quadrature | Hardy's rule | Lagrange interpolating polynomial | numerical integration | Shovelton's rule | Simpson's 3/8 rule | Simpson's rule | trapezoidal rule | Weddle's rule | Woolhouse's formulas

Isaac Newton | Roger Cotes