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交换积分∫0%>1Dy∫3 %>3y E^x^2Dx的次序

如图所示: 如果你只是想要转换结果的话,红色框那就可以止步了。

I=∫(0,1)x^2dx∫(x,1)(e^(-y^2))dy =∫(0,1)e^(-y^2)dy∫(0,y)x^2dx =1/3∫(0,1)y^3*e^(-y^2)dy =-1/6∫(0,1)y^2*d(e^(-y^2)) =-1/6y^2*e^(-y^2)[0,1]+1/3∫(0,1)y*e^(-y^2)dy =-1/(6e)-1/6e^(-y^2)[0,1] =-1/(6e)-1/(6e)+1/6 =1/6-1/(3e)

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