∫∫e^(x+y)dxdy,积分区域为x=0,y=0,x+y=1所围成的区域紧急啊~~~!!!!!!!!拜托拜托~~~~!!!!!

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∫∫e^(x+y)dxdy,积分区域为x=0,y=0,x+y=1所围成的区域紧急啊~~~!!!!!!!!拜托拜托~~~~!!!!!∫∫e^(x+y)dxdy,积分区域为x=0,y=0,x+y=1所围成

∫∫e^(x+y)dxdy,积分区域为x=0,y=0,x+y=1所围成的区域紧急啊~~~!!!!!!!!拜托拜托~~~~!!!!!
∫∫e^(x+y)dxdy,积分区域为x=0,y=0,x+y=1所围成的区域
紧急啊~~~!!!!!!!!拜托拜托~~~~!!!!!

∫∫e^(x+y)dxdy,积分区域为x=0,y=0,x+y=1所围成的区域紧急啊~~~!!!!!!!!拜托拜托~~~~!!!!!
∫∫e^(x+y)dxdy
=∫[0,1] dx ∫[0,1-x] e^x*e^y dy
=∫[0,1] e^x dx ∫[0,1-x] e^y dy
=∫[0,1] e^x dx (e^y |[0,1-x])
=∫[0,1] e^x(e^(1-x)-1) dx
=∫[0,1] (e-e^x) dx
= (ex-e^x) |[0,1]
= e