计算积分∫∫ e^x^2dxdy,其中D是由曲线y=x^3与直线y=x在第一象限内围成的闭区域

曲线y=x^3与直线y=x的交点（0,0）（1,1）
∫[0,1]e^x^2∫[x^3,x] dxdy
=∫[0,1]e^x^2*(x-x^3)dx
=1/2e^x^2[0,1]-1/2∫[0,1]e^x^2*x^2dx^2
=1/2e^x^2[0,1]-1/2e^x^2*x^2[0,1]+∫[0,1]e^x^2dx^2
=1/2e^x^2[0,1]-1/2e^x^2*x^2[0,1]+e^x^2[0,1]
=e/2=e/2+e-1
=e-1

∫{0，1}dx∫{x^3,x}e^{x^2}dy=0.5∫{0,1}e^{x^2}(1-x^2)dx^2
=0.5∫{0,1}(1-x)e^xdx.