Abstract
This chapter discusses the basic properties of numerical integration. The numerical integration (quadrature) formulas that follow are of the form I= ∫baf(x)dx = Σnk = 0w(n)kf(xk) + Rn, with a ≤ x0< x1 < · ·· < xn ≤ b. The weight coefficients and the abscissas xk, with k = 0, 1 , … , n are known numbers independent of f(x) that are determined by the numerical integration method to be used and the number of points at which f(x) is to be evaluated. The remainder term, Rn when added to the summation, makes the result exact. The precise value of Rn is unknown; its analytical form is usually known and can be used to determine an upper bound to |Rn| in terms of n. An integration formula is said to be of the closed type if it requires the function values to be determined at the end points of the interval of integration, so that x0= a.
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