我們提出一個Gruess型態積分不等式，它是建立在兩個分別為遞增型態與r-Hoelder型態之函數上，並提出遞增型態之函數在擾動梯形公式與類梯形公式之數值積分上的應用例子。

We give an integral inequality of Gruess' type for two mappings of increasing type and of r-Hoelder's type. We also provide the applications for perturbed trapezoid formula and quasi-trapezoid formula and examples in numerical integration.

1. Introduction                           1
2. Main Theory                            3
3. Application for Trapezoid Formula      5
References                               13

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