10楼: Originally posted by peterflyer at 2015-12-16 17:40:10
用极坐标求解。
被积函数=arctan*r*dr*dθ
      =θ*r*dr*dθ
故原积分=Integral{{dθ, -π/2, π/2}*Integral{θ*r*dr , 0 , 4*Cosθ}}
=2*π^2

10楼: Originally posted by peterflyer at 2015-12-16 17:40:10
用极坐标求解。
被积函数=arctan*r*dr*dθ
      =θ*r*dr*dθ
故原积分=Integral{{dθ, -π/2, π/2}*Integral{θ*r*dr , 0 , 4*Cosθ}}
=2*π^2