# ON AN ERROR OF TRAPEZOIDAL RULE

• Hong, Bum-Il (Department of Mathematics Kyung Hee University) ;
• Choi, Sung-Hee (Division of Information and Computer Science Sun Moon University) ;
• Hahm, Nahm-Woo (Institute of Natural Science Kyung Hee University)
• Published : 1998.10.01

#### Abstract

We show that if r $\leq$ 2, the average error of the Trapezoidal rule is proportional to $n^{-min{r＋l, 3}}$ where n is the number of mesh points on the interval [D, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when r $\leq$ 2.