直線近似による数値積分公式とその誤差評価

Abstract

In the classical integration formulae such as the mensuration by parts, the trapezoid rule and the midpoint rule, the curve y=f(x) is approximated by the straight lines and hence the calculations are relatively simple. The main purpose of this study is to introduce several new integration formulae approximated by various straight lines passing the points on the curve y=f(x) . At the same time, we shall give the error estimations concerning the new integration formulae.