广义积分:定积分在极限思想下的自然延伸

GENERALIZED INTEGRAL:DEFINITE INTEGRAL’S NATURAL EXTENSION IN THEORY OF LIMITS

研究函数在某区间上的定积分时,总是假定区间为有限区间,并且函数为该区间上的有界函数。如果去掉这两个限制,则得到无穷区间上有界函数的广义积分与有限区间上无界函数的广义积分。一般对这两类广义积分概念的引入缺乏直观性。

When function's definite integral at a certain interval is studied, limited interval is hypothesized, function is thought to be bounded function. Without these two restrictions, bounded function's generalized integral at the limitless intervals and unbounded function's generalized integra' at the limited intrvals will be achieved. Generally speaking, their conceptions are not directly perceived. In this paper, several examples are illustrated to explain the natural rationality of extending from definite integral to generalized integral.