x=0,y=1,y=x,求双重积分∫ ∫(x^2)(e^(-y^2))dxdy..

先积x
∫ [0-->1]∫ [0-->y] x²e^(-y²)dxdy
=∫ [0-->1]1/3x³e^(-y²)| [0-->y] dy
=1/3∫ [0-->1]y³e^(-y²)dy
=1/6∫ [0-->1]y²e^(-y²)d(y²)
令y²=u,u：0-->1
=1/6∫ [0-->1] ue^(-u)du
=-1/6∫ [0-->1] ude^(-u)
=-1/6ue^(-u)+1/6∫ [0-->1] e^(-u)du
=-1/6ue^(-u)-1/6e^(-u) [0-->1]
=1/6-1/6e^(-1)-1/6e^(-1)
=(e-2)/(6e)