有限极限的广义反常积分定义
Generalized improper integral definition for finite limit
摘要：
给出了一维有限极限反常积分定义的推广。新的定义扩展了有效积分的范围，包括以前被认为是不可积的积分。通过对积分变量的特殊变量变换，证明了该定义与“广义反常积分无穷极限定义”（arXiv：0805.3559）中的无穷极限定义是等价的.定义保持线性和唯一性。在传统定义下有效的积分在新定义下具有相同的值。交换的积分和微分的顺序，并与第二个积分交换的顺序，得到的标准。提供了实例。
英文摘要：
A generalization of the definition of a one-dimensional improper integral with a finite limit is presented. The new definition extends the range of valid integrals to include integrals which were previously considered to not be integrable. This definition is shown to be equivalent to the infinite limit definition presented in "Generalized improper integral definition for infinite limit" (arXiv:0805.3559) via a particular change of variable of integration. The definition preserves linearity and uniqueness. Integrals which are valid under the conventional definition have the same value under the new definition. Criteria for interchanging the order of integration and differentiation, and for interchanging the order with a second integration, are obtained. Examples are provided.
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