∫∫(x^2/y^2)dxdy,其中D为直线y=x,y=2和双曲线xy=1所围成的区域, 计算二重积

联立解 y=x,xy=1,得第一象限交点 (1,1),则
∫∫ x^2/y^2dxdy = ∫(1/y^2)dy∫ x^2dx
= ∫ 1/y^2dy[x^3/3]∫
= (1/3)∫ (y-1/y^5)dy
= (1/3)[y^2/2+1/(4y^4)] = 27/64