Then

Abstract. An error runs through a paper by Cerone and Dragomir [1] is corrected. Thus enable us to get a right form of a trapezoidal type rule for weighted integrals and its applications in numerical integration. 1. Preliminaries Some definitions are required to simplify the subsequent work. Definition 1. Let ω(x) be a positive integrable function on [a, b]. Let µ and ν be its zeroth and first moments about zero so that µ = ∫ b a ω(x)dx < ∞ (1.1) and ν = ∫ b a xω(x)dx < ∞ (1.2) Definition 2. P and Q will be used to denote the zeroth and first moments of ω(x) over a subinterval [a, b]. In particular, for λ> 0 the subscript a or b will be used to indicate the intervals [a, a+ λ] and [b − λ, b] respectively. Thus, for example