求教,倒数第二步是怎么变成最后一步的??ex2⼀2(-无穷→+无穷)不是等于根号π吗?

2025-05-12 23:51:03
推荐回答(1个)
回答1:

t=x-2
dt= dx
x=-∞ , t->-∞
x=+∞ , t->+∞
∫(-∞->+∞) (x-2+2) e^[-(x-2)^2/2] dx
=∫(-∞->+∞) (x-2) e^[-(x-2)^2/2] dx +2∫(-∞->+∞) e^[-(x-2)^2/2] dx
=∫(-∞->+∞) t e^[-t^2/2] dt +2∫(-∞->+∞) e^[-t^2/2] dt