∫x^2dx/根号下a^2-x^2=?请尽可能详细,

Question

∫x^2dx/根号下a^2-x^2=?请尽可能详细,

Answer 1

∫x^2/√(a^2-x^2) dx令x=a·sin u ,则原积分=|a|·∫sin^2 u /√(cos^2 u) d(a·sin u)=a^2·∫sin^2 u(cos u /|cos u|) du=a^2·∫sin^2 u du =a^2·∫(1-cos 2u)/2 du=(a^2/4)·∫(1-cos 2u) d(2u)=(a^2/4)·(2u ...