Quadrature formulae with the weight functionX1/2

Abstract

The method of undetermined coefficients is used to establish the third, fourth and fifth degree formulae with respect to the weight function x 1/2 where the region of integration is the space Ω = [(x y): 0≦ x≦ l and −l≦ y≦ l]. Since the minimum number of points in numerical integrations are very important, we note that the fourth degree formulae does not attain the minimum points while the fifth degree formula does. We prove that the minimum points for the fifth degree formula is attained by constructing the same fifth degree formula using Radon's method [4]. However, in future we shall investigate an alternative approach for the possibility of constructing a fourth degree formula with least points, see [5].