Focus On . . . : No. 35

[摘要] Focus On... No 10 [2014 : 21-24] considered the integrals In =Z 10( (x))n dx,where the quadratic function(x) = ax2 +bx+c was supposed to remain positivein [0; 1]. The study culminated in the asymptotic behavior of such integrals, thatis, the determination of a simple sequence (!n) such that limn!1In!n= 1, denoted byIn !n. In this number, we keep the same goal but, through various sequencesof integrals, present some simple ways to obtain such an asymptotic behavior. Werestrict ourselves to elementary problems and methods, referring the reader to[1] for more complicated examples and to [2] for more sophisticated techniques(Laplace's method, for instance).

[学科分类] 数学（综合）