I = ...... = -3∫∫∫<∑> (x^2/a^2 + y^2/b^2 + z^2/c^2)dxdydz
作广义球坐标变换 x = arsinφcosθ, x = brsinφsinθ, z = crcosφ
I = -3∫<0 ,π>dφ∫<0, 2π>dθ∫<0, 1>r^2 abcr^2sinφdr
= -3abc∫<0, π> sinφdφ∫<0, 2π>dθ∫<0, 1>r^4dr
= -3abc*2π[-cosφ]<0, π>[r^5/5]<0, 1> = (12/5)πabc
内容全部来源于网络收集，如有侵权，请联系网站删除！