求广义积分:x乘以[e的(-x的2次方)]dx,上限是(正无穷),下限是0?

问题描述:

求广义积分:x乘以[e的(-x的2次方)]dx,上限是(正无穷),下限是0?
$(acontent)

∫(0,∞ )x*e^(-x^2)dx
=1/2∫(0,∞ ) e^(-x^2)d(x^2)
=-1/2*e^(-x^2) (0,∞)
=(-1/2)*(0-1)
=1/2