摘要
由连续单调函数的几何意义直观地得出一个不等式,即若设函数f(x)在[0,b]上连续且单调递减,则有b∫a0f(x)dx≥a∫b0f(x)dx(0≤a≤b).通过构造辅助函数给出其数学证明,并对其加以推广.
Inspired by its geometric obvio＇us, the integral inequalityb∫0^af（x）dx≥a∫0^bf（x）dx（0≤a≤b）.where f（x） is continuous and monotone decreasing on the interval [0, b], is provedby constructing a proper auxiliary function.
出处
《高等数学研究》
2013年第6期59-59,共1页
Studies in College Mathematics
关键词
连续单调函数
几何意义
积分不等式
continuous and monotone decreasing function, geometric view, integral inequality
