Quadrature Formulas

formulas for approximating definite integrals by means of the values of the integrand at a finite number of points. The most common quadrature formulas have the form

where x₁x₂, …, x_n are the nodes of the quadrature formula, A₁, A₂ . . . ,A_n are its coefficients, and R_n is the remainder term. For example,

where a ≤ ξ ≤ b (trapezoidal rule). Sometimes for mulas for mechanical, or numerical, quadrature are also called quadrature formulas.