牛顿积分与黎曼积分之异同

Similarities and Differences between Newton Integral and Riemann Integral

牛顿所积分的函数都是连续的,可分为牛顿不定积分和牛顿定积分,而黎曼所积分的函数又是有界的。因此,并不是每一个牛顿不定积分都可进行黎曼积分,并不是每个黎曼积分都存在牛顿不定积分,黎曼积分也并不能对每一个有界函数求定积分。只有连续函数在闭区间上的黎曼和牛顿不定积分与定积分都存在时方可积分。

Newton integral, which can be divided into the indefinite integral and the definite integral, is used for continuous function, while Riemann integral is used for the limited function. Therefore, it is not every Newton indefinite integral that can carry on Riemann integral, and not every Riemann integral has Newton Indefinite integral Riemann integral can not be used in every limited function to get its definite integral The functions can be integrlized only when the continuous functions in their closing area have both Newton integral and Riemam integral.