同时利用带位的奇异积分方程理论得到了这一问题可解的主要条件及指数计算公式。

By the singular integral equation theory we obtain the resolvable sufficient and necessary condition and the formula of counting index for the problem.

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文章利用达布和理论，讨论了黎曼积分的可积性问题，给出了一个可积的充分必要条件。

Based on Darboux theory, this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability.

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分析了诸多积分概念的共性，抽象出黎曼积分的定义，给出了黎曼可积的条件。

This paper sums up the common character of the concept of many integrals, abstracts the concept of Riemann integral and gives the integral conditions of the Riemann integral.

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