两类积分的求解

The Solution about Two Types of Integration

讨论了两类积分的求解问题.对于积分I1=∫+∞-∞e-ax2dx,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=∫c2c1e-a(x-b)2dx,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.

The solution methods about two types of integration were discussed. For the integration I1=∫＋∞-∞e-ax2dx 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 I1=∫＋∞-∞e-ax2dx,a〉0,b,c1,c2which are arbitrary real number, by constructing normal density and checking probability distribution table to solve .