2sVhJDv81RbJDtk0abRE28jWvaWSrH+nQFn0GsChZdvXSziuIYNDWxubxNL4Zc2ZHBZ9Vpzpkjub a63ieOkig1hIzDG4UFvzOTumTv0aNuScfEfnEHEZLO1Pd0a3P22ZGlQjzHLp9cZrxhQgWRGTyUt8 zpZsHsM6nPz9kDPt9MSPcaYWMcdeQFx6DoilBj/dg9J+0Ztc5EYs1Sz8uLo1IojrtsGeKOvA7fuT a7+aK7gq10YpEwuf8uy4gXGLrYHNGb0P62YOC...
H4XtvPmi6KjgEhnWWgxA32ZDvjPOCJH5CG7bEgrGEu+4Xlxpdg3SzIftraY76bqEL1UiJ4Qc7+bn TKlnJZnRIxW1aAA9FKO51Uol+LxN+mPVnQinghVpTK+RTrYPTcwv7RVCCIPOFrcaYdCudYBC7baC 2pODeFCTYCDouV050tqN1GV5mYlnQXF9eVcF3PY5shqWzBCtYUsbz7KEAv6cCZ2YsSlPoDpG3Pqd kbiMIxUQ2rgISnCuUKpZpNQfFSFmG7I8y53Vjw...
[1]:data:image/jpg;base64,iVBORw0KGgoAAAANSUhEUgAAAXgAAAMMCAYAAABZsbxYAAAABHNCSVQICAgIfAhkiAAAABl0RVh0 U29mdHdhcmUAZ25vbWUtc2NyZWVuc2hvdO8Dvz4AACAASURBVHic7N13mBRF+sDxb3dP3sDukkEy SFBAQREURUAMBMWEIpizHvrzTOedWUynh+HOcCYw4AEmQBEwgIqnIooCAhIUBcmweSd39++PmrCZ TaS59/M8POz0dFdV98y8X...
简单分析一下，详情如图所示
∫∫∫(Ω)(x+y+z)dv =∫∫∫(Ω)xdv+∫∫∫(Ω)ydv+∫∫∫(Ω)zdv 由于对称性，x,y,z都是奇函数， 则积分为零。如果一定要化为三次积分，用球坐标计算如下：∫∫∫<Ω>(x+y+z)dv = ∫<0,π>dφ∫<0,2π>dθ∫<0,r>ρ(sinφcosθ+sinφsinθ+cosφ)ρdρ = (r^...
O!^N{QLgSOsphxH3PuAc!Et9!9J;kCK`Y&zpzozEn4n^R5F0+%qB z{Yk#44MITTT<+JBD9qV_dd0Fov`SD6eEUA-XT`gM^jW{soX9rS-gUZStNVU$)3edD zx^FoEPiP@fZ+DOy+KCT$XunqiV|P|mfhT=`>AZa7#n|a97{1z?^!?|C`d2%u)c2Xb z)XnOi#Sz|TqmMcJC+v45i>b^9X6MD~3>kv#cjBvlChueRUs`L8no{tOZ>...
由积分区域的对称性化简（详细见全书，上面有归纳）,先面积分后对z积分，因为被积函数无xy，由圆面积公式得：∫∫∫1/z dV=∫∫∫1/z(PI(2-z^2)dz=PI(ln2-1/2)
∫∫∫(Ω)(x+y+z)dv =∫∫∫(Ω)xdv+∫∫∫(Ω)ydv+∫∫∫(Ω)zdv 由于对称性，x,y,z都是奇函数， 则积分为零。如果一定要化为三次积分，用球坐标计算如下：∫∫∫<Ω>(x+y+z)dv = ∫<0,π>dφ∫<0,2π>dθ∫<0,r>ρ(sinφcosθ+sinφsinθ+cosφ)ρdρ = (r^...
如图所示：
百度试题 题目9.计算zdV,其中(O) = {(x,y,z) |x2+y2+(z-a)2≤a2,x2+y2≤2(a> 0)}() 相关知识点: 解析反馈 收藏