第一型曲线积分的可积性条件及其应用

Integrable Condition of the First Type Curve Integral and Its Application

类比定积分可积性条件,给出了第一型曲线积分的上和与下和概念,并通过研究上和与下和的性质,得到了第一型曲线积分的可积性条件(包括必要条件、充分条件和充要条件)及其性质,完善了第一型曲线积分可积性理论。在文章最后给出了第一型曲线积分性质的简单应用。

Through analog integral integrability conditions, this paper gives concept of upper and lower sum for the first type curve integral. The integrability conditions including the necessary and sufficient conditions are obtained. Theory of the first type curve integral integrability is improved. At the end of the paper, a simple application of the integral property of the first type curve integral is given.