等价无穷小在变上限积分的加(减)运算中的替换

Equivalent Infinitesimals of Integrals of Variable Upper Bounds and Sum or Difference

本文探讨了当一元变上限积分函数的上限为无穷小,且被积函数为两个无穷小的和(差)运算时,在满足一定条件下,分别对积分上限以及被积函数中的无穷小应用等价无穷小替换,则替换前后的积分是等价无穷小.

This paper proves that if the upper bound of an integral is an infinitesimal and the integrand function is the sum or difference of two infinitesimals,under certain condition the following replacement yields equivalent infinitesimals:replacing the upper bound and the sum or difference of integrand functions,respectively,by other equivalent infinitesimals.