菏泽学院学报
菏澤學院學報
하택학원학보
JOURNAL OF HEZE UNIVERSITY
2014年
5期
91-94
,共4页
积分%求解%重积分法%伽玛函数法%概率方法%概率分布
積分%求解%重積分法%伽瑪函數法%概率方法%概率分佈
적분%구해%중적분법%가마함수법%개솔방법%개솔분포
integral%solution%multiple integration method%Gama function method%probabilistic method%probability distribution
讨论了两类积分的求解问题。对于积分I1＝∫＋∞-∞e-ax2 dx，其中a ＞0为常数，给出了以下几种求解方法：利用它与重积分的关系给出两种解法；利用此类积分的特点巧妙借助伽玛函数给出一种求解方法；根据被积函数的特点和积分区域的特殊性来构造恰当的概率分布求解。对于积分I2＝∫c2 c1 e-a（ x-b）2 dx，其中a ＞0，b，c1，c2为任意实数，通过构造正态密度和查概率分布表求解。
討論瞭兩類積分的求解問題。對于積分I1＝∫＋∞-∞e-ax2 dx，其中a ＞0為常數，給齣瞭以下幾種求解方法：利用它與重積分的關繫給齣兩種解法；利用此類積分的特點巧妙藉助伽瑪函數給齣一種求解方法；根據被積函數的特點和積分區域的特殊性來構造恰噹的概率分佈求解。對于積分I2＝∫c2 c1 e-a（ x-b）2 dx，其中a ＞0，b，c1，c2為任意實數，通過構造正態密度和查概率分佈錶求解。
토론료량류적분적구해문제。대우적분I1＝∫＋∞-∞e-ax2 dx，기중a ＞0위상수，급출료이하궤충구해방법：이용타여중적분적관계급출량충해법；이용차류적분적특점교묘차조가마함수급출일충구해방법；근거피적함수적특점화적분구역적특수성래구조흡당적개솔분포구해。대우적분I2＝∫c2 c1 e-a（ x-b）2 dx，기중a ＞0，b，c1，c2위임의실수，통과구조정태밀도화사개솔분포표구해。
The solution methods about two types of integration were discussed .For the integration I1 =∫+∞-∞e-ax2 dx, a >0 , which is a constant , given some methods for solving as following:two solution methods were given by using the relationship with multiple integration;noting its features we found a skilful method based on Ga-ma function;we got a solution method of probability theory through constructing a proper probability distribution . For the integration I2 =∫c2 c1 e-a(x-b)2dx,a >0,b,c1,c2 which are arbitrary real number , by constructing normal densi-ty and checking probability distribution table to solve .
