用极坐标代换
在圆x^2+y^2=1和圆(x-1)^2+y^2=1内f=√（x²+y²）-1=r-1
在圆x^2+y^2=1外,圆(x-1)^2+y^2=1内f=1-√（x²+y²）=1-r
I=∫[-π/3,π/3]dθ(∫[0,1](r-1)rdr+∫[1,2cosθ](1-r)rdr)+(∫[-π/2,-π/3]+∫[π/3,π/2])dθ∫[0,2cosθ](r-1)rdr
=π/3-4+3√3/2