关于分段连续函数的原函数的连续性及其应用

On the Original Functional Continuity of Sectional-continuous Function and Its Application

区别x0为分段连续函数f(x)的间断点的不同类型,给出了其原函数F(x)在x0处是否连续的充分条件,且揭示了各段上的积分常数之间的相互关系,对分段函数的不定积分计算提供了理论依据.

X0 as different types of discontinuous point of sectional-continuous function f（x） is discriminated in this article. And the sufficient condition of whether its original function F（x） is continuous at the point x0 is given here. Meanwhile, the interrelations of integral constants at different sections are revealed, which provides theoretical basis for the calculation of indefinite integral of sectional function.