积分中值定理中间点的渐近估计式

Asymptotic Estimation Formulas of the Intermediate Point for Integral Mean Value Theorem

利用在无穷区间上的比较函数概念,在g(x)可积的较弱条件下,建立了第一、二积分中值定理"中间点"当x→+∞时更广泛的渐近估计式,作为推论得到了Cauchy中值定理和Taylor中值定理的"中间点"当x→+∞时的渐近估计式,从而统一和发展了有关文献的结果.

By using the comparison function in infinite interval, under weaker conditions of g（x） integrable, more extensive asymptotic estimation formulas of the ＂intermediate point＂ in the first integral mean value theorem and the second integral mean value theorem are established when x is near ＋ ∞ , as the corollaries, the asymptotic estimation formulas of the ＂intermediate point＂ of the Cauchy mean value theorem and the Taylor mean value theorem are obtained, which unify and extend corresponding results of some references.