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 On an Error of Trapeziodal Rule Commun. Korean Math. Soc. 1998 Vol. 13, No. 4, 903-911 Bum Il Hong, Sung Hee Choi, Nahmwoo Hahm Department of Mathematics, Sun Moon University, Kyung Hee University Abstract : We show that if $r\le 2$, the average error of the Trapezoidal rule is proportional to $n^{-\min\{r+1,\ 3\}}$ where $n$ is the number of mesh points on the interval $[0,\ 1]$. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when $r\le 2$. Keywords : MSC numbers : 65D30, 65G10, 28C20 Downloads: Full-text PDF