This paper proves the necessary and safficient condition of uniform convergence of infinite integral with parameters,and discusses the feature of unifom convergence of infinite integral with parameters,explains its application with examples.

On the base of the relation between the two abnormality integral containing parameters, the judgment theorem of consistent astringency of flaw integral containing parameters was deduced from the judgment theorem of consistent astringency infinite integral containing parameters.

Containing Parameter Integral and Uniform Convergence on Fuzzy Interval Value Function

Four Methods of Solution for Infinite Integral I=integral from n=-∞ to +∞(e~(-x)~2dx);

The demonstration of equivalence between two infinite integral convegence;

Analysis on the Convergent Sufficiency of the Infinite Integral s Integrand;

We give some formulas for a class improper integrals integral from n=0 to ∞()(sin~r(αx)/x~s)cos~p(bx),for α≠0,b≥0,r,s,p∈N={1,2,3,…}.

In the article,some evaluations for the first kind of improper integrals ∫~∞_0sin(βx)x~ncos(bx)dx for positive integer n1 and real numbers β≠0,b0 are established using the trigonometric power formulae, the L′Hospital rule,integration by part,and mathematical induction.

On the base of the relation between the two abnormality integral containing parameters, the judgment theorem of consistent astringency of flaw integral containing parameters was deduced from the judgment theorem of consistent astringency infinite integral containing parameters.