I = ∫∫ (D is the integral region) | √ (X & # 178; + Y & # 178;) - 1| D σ is calculated. The region D is surrounded by the curve y = √ (2x-x & # 178;) and X axis

I = ∫∫ (D is the integral region) | √ (X & # 178; + Y & # 178;) - 1| D σ is calculated. The region D is surrounded by the curve y = √ (2x-x & # 178;) and X axis

Substitution with polar coordinates
In circle x ^ 2 + y ^ 2 = 1 and circle (x-1) ^ 2 + y ^ 2 = 1, f = √ (X & # 178; + Y & # 178;) - 1 = R-1
Outside the circle x ^ 2 + y ^ 2 = 1, inside the circle (x-1) ^ 2 + y ^ 2 = 1, f = 1 - √ (X & # 178; + Y & # 178;) = 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