作业帮求教高数
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/10 18:04:16
求教高数
求教高数
求教高数
积分顺序改成x,z,y
I=∫(0,1)(1-y)dy∫(0,1-y)dz∫(0,1-y-z)e^(-(1-y-z)^2)dx
=∫(0,1)(1-y)dy∫(0,1-y)(1-y-z)e^(-(1-y-z)^2)dz
=(1/2)∫(0,1)(1-y)dy∫(0,1-y)e^(-(1-y-z)^2)d(-(1-y-z)^2)
=.
没问题啦?
转换积分次序
I= ∫<0,1> ∫<0,1-y> ∫<0,1-z-y> (1-y)e^[-(1-y-z)] dx dz dy
=∫<0,1> (1-y) ∫ <0,1-y> (1-z-y) e^[-(1-y-z)] dz dy
=∫<0,1> (1-y) *{[1-(z+y-1)]*e^(y+z-1)|<0,1-y> }dy
= ∫<0,1> (1-y) *[1-...
全部展开
转换积分次序
I= ∫<0,1> ∫<0,1-y> ∫<0,1-z-y> (1-y)e^[-(1-y-z)] dx dz dy
=∫<0,1> (1-y) ∫ <0,1-y> (1-z-y) e^[-(1-y-z)] dz dy
=∫<0,1> (1-y) *{[1-(z+y-1)]*e^(y+z-1)|<0,1-y> }dy
= ∫<0,1> (1-y) *[1-(2-y)e^(y-1)]dy
= -(1-y)²/2|<0,1> -∫<0,1> (1-y) *(2-y)e^(y-1)dy
=1/2 -1/e*∫<0,1> (y²-3y+2)e^ydy
=1/2-1/e*(y²-5y+7)e^y|<0,1>
=1/2+7/e-3=7/e-5/2
收起