含参量定积分n^p∫~1_0x^nf(x)dx和∫~1_0φ(x,t)f(x)dx的极限问题  

Limit problems for involving parametric definite integrals n^p ∫~1_0 x^n f(x)dx and ∫~1_0 φ ( x , t ) f ( x ) dx

作　　者：李晓萍[1] 王钦[2] 李睿芳[3] 

机构地区：[1]天津师范大学管理学院,天津300387 [2]内蒙古农业大学计算机与信息工程学院,内蒙古呼和浩特010018 [3]内蒙古农业大学水利与土木建筑工程学院,内蒙古呼和浩特010018

出　　处：《新疆师范大学学报（自然科学版）》2013年第1期43-47,共5页Journal of Xinjiang Normal University(Natural Sciences Edition)

摘　　要：针对两类特定型含参量定积分的极限问题。首先,依据函数在某端点的连续性将定义域分割成两部分,并在该端点的局部邻域上建立一个与被积函数相关的不等式。其次,通过实例和应用定积分的可加性、单调性和极限的夹逼定理获得该特定型含参量定积分的极限值。Aim at the limit problems of two specific types definite integrals involving parameters. Firstly,thedefinition domain is divided into two parts in the light of the continuity of functions at one end point . Secondly, an inequality responding to the integrand function is established at the local regions of this end point, and the limit values of the specific types definite integrals involving a parameter are ob- tained by applying the additivity and monotonicity of definite integrals as well as the approximation theo- rems of limits by some examples.

关 键 词：含参量定积分 单调性 极限问题 

分 类 号：O211.4[理学—概率论与数理统计]