International Journal of Mathematical Analysis Vol. 14, 2020, no. 3, 109 - 115 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2020.91288 The Lebesgue Integral of Trapezoid Rule Based on Derivative Atia Rehman Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan Khurrem Shehzad Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan Fatima Noreen Department of Mathematics and Statistics University of Agriculture Faisalabad, Pakistan This article is distributed under the Creative Commons by-nc-nd Attribution License. Copyright c  2020 Hikari Ltd. Abstract In this paper the trapezoid rule for lebesgue integral based on deriva- tive estimated. In which the use of derivative based lebesgue integral at the terminals. This category of quadrature formula acquires an exact- ness of two order along lebesgue integral of trapezoid rule and explores by an inappropriate numbers. At the end, the conception of trapezoid rule for lebesgue integral indicated. Keywords: Numerical Integration; Lebesgue Integral, Riemann Stieltjes Integral, Quadrature Rule, Trapezoid Rule, Degree of Precision, Error term 1 Introduction Numerical integration tends to determine the numerical inaccuracy for several rates of S, then f (x) is defined by area A under the curve [8]. In numerical