得用极坐标x=rcosty=rsintx^2+y^2=r^2r:[0,1]t:[0,pi/2]dxdy=rdr还是四分之一,因为只有第一象限∫(0,1)∫(0,1)e^(x^2+y^2)dxdy=∫(0,pi/2)∫(0,1)e^(r^2)rdrdt=pi/2*(1/2)∫(0,1)e^(r^2)d(r^2)=pi/4*e^(r^2)|[0,1]=(pi/4)(e-1)=pi(e-1)/4