求这道重积分怎么解？
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区域D可以表示为由x=y^2，x=1，y=0围成的闭区域
原式=∫(0,1)dy*∫(y^2,1)e^[-(y^2)/2]dx
=∫(0,1)e^[-(y^2)/2]*(1-y^2)dy
=∫(0,1)e^[-(y^2)/2]dy-∫(0,1)e^[-(y^2)/2]*y^2dy
=e^[-(y^2)/2]*y|(0,1)-∫(0,1)yd{e^[-(y^2)/2]}-∫(0,1)e^[-(y^2)/2]*y^2dy
=e^(-1/2)-∫(0,1)e^[-(y^2)/2]*(-y^2)dy-∫(0,1)e^[-(y^2)/2]*y^2dy
=e^(-1/2)
原式=∫(0,1)dy*∫(y^2,1)e^[-(y^2)/2]dx
=∫(0,1)e^[-(y^2)/2]*(1-y^2)dy
=∫(0,1)e^[-(y^2)/2]dy-∫(0,1)e^[-(y^2)/2]*y^2dy
=e^[-(y^2)/2]*y|(0,1)-∫(0,1)yd{e^[-(y^2)/2]}-∫(0,1)e^[-(y^2)/2]*y^2dy
=e^(-1/2)-∫(0,1)e^[-(y^2)/2]*(-y^2)dy-∫(0,1)e^[-(y^2)/2]*y^2dy
=e^(-1/2)
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