计算I=∫∫1/(x2+y2+z2)dS,S是抛物面z=x2+y2与平面z=1所围立体的外表面
问题描述：
计算I=∫∫1/(x2+y2+z2)dS,S是抛物面z=x2+y2与平面z=1所围立体的外表面
答
dS=√(1+4x^2+4y^2)dxdy,投影：x^2+y^2《1I=∫∫1/(x^2+y^2+(x^2+y^2)^2)*√(1+4x^2+4y^2)dxdy+∫∫1/(x^2+y^2+1)*dxdy用极坐标：=∫(0,2π)dθ∫(0,1)r√(1+4r^2)dr/(r^2+r^4)+∫(0,2π)dθ∫(0,1)rdr/(r^2+1)=π∫...