二重积分的计算 题目是求∫∫（e的y/x次方）dxdy 其中D是由曲线y=x^2直线y=x以及x=1

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∫∫（e^(y/x）dxdy
=∫[0,1/2] dx∫[x^2,x] （e^(y/x）dy
=∫[0,1/2] dx {（xe^(y/x）|[x^2,x]}
=∫[0,1/2] (xe-xe^x) dx
=ex^2/2|[0,1/2] -∫[0,1/2] xe^xdx
=e/8 -∫[0,1/2] xde^x
=e/8 - xe^x|[0,1/2]+∫[0,1/2] e^xdx
=e/8-√e/2 +[√e -1]
=e/8 +√e/2 -1