Abstract: Inequalities are widely used in mathematical research and practice.This paper analyses the problems of proving inequalities in the Undergraduate’s Mathematical Contest.Based on the method of constructing auxiliary functions and Cauchy’s mean value theorem,more general integral inequalities are established,which generalize the inequalities appearing in Undergraduate’s Mathematical Contest and the inequalities in the existing literature. 

Key words: Auxiliary function, Integral inequality , Cauchy’s mean value theorem, Undergraduate’s Mathematical Contest