函数$begin{eqnarray}f(x,y)=begin{cases}frac{x^2y^2}{x^4+y^4},&(x,y)eq(0,0)cr0,&(x,y)=(0,0)end{cases}end{eqnarray}$在点$(0,0)$处
设区域$D={(x,y)midx^2+y^2leqy,xgeq0}$,利用极坐标变换重积分$$int!!!!int_Df(x,y)dxdy=int_0^{2pi}dthetaint_0^{sintheta}f(rcostheta,rsintheta)rdr.$$
$$int!!!!int_Df(x,y)dxdy=int_0^{frac{pi}{2}}dthetaint_0^{sintheta}f(rcostheta,rsintheta)rdr.$$