求教高数
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/13 00:28:06
![求教高数](/uploads/image/z/3794452-52-2.jpg?t=%E6%B1%82%E6%95%99%E9%AB%98%E6%95%B0)
xn@_
*3_',`3T-=vcȘVB P6(tZED/dScO,fcgi>~[O
=p
&I{aqCHN7 ^~xnD*~}𨷢2!\A7-AmluL˃eT?mp`BOǀ`"Z]G&cC?Uozݘ\({1^,Or]V#bhBՀ>r!
].w{c6zQLNW|zN۴5:a[DUaөS)Xeu$aE/ŅT)QHZ1Z>O7lݪ7T>?'X-B2-Z^P @tl2P7m>^Ue1mQY֚ltJܩ֜02NQEgg8\;ੱ*+]b:@;YF{d3ydk¥כZ)@~S˷?%
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