∫e^(-x^2)dx=√π,用二重积分怎么证明

∫e^(-x^2)dx=∫e^(-y^2)dy而∫e^(-x^2)dx*∫e^(-y^2)dy=∫∫e^(-y^2)*e^(-x^2)dxdy=∫∫e^(-x^2-y^2)dxdy然后是用极坐标换元,x=rcosa,y=rsinar属于[0,无穷大),a属于[0,2π]=∫∫re^(-r^2)drda (r属于[0,无穷...