∫ (X & ∫ 178; + Y & ∫ 178;) ds ∑: z = root X & ∫ + Y & ∫ 178; the part cut off by z = 2 ∫ ∫ is followed by ∑

∫ (X & ∫ 178; + Y & ∫ 178;) ds ∑: z = root X & ∫ + Y & ∫ 178; the part cut off by z = 2 ∫ ∫ is followed by ∑

∵ z = √ (X & # 178; + Y & # 178;), then α Z / α x = x / √ (X & # 178; + Y & # 178;), α Z / α y = Y / √ (X & # 178; + Y & # 178;)
∴ds=√[1+(αz/αx)²+(αz/αy)²]dxdy
=√[1+(x/√(x²+y²))²+(y/√(x²+y²))²]dxdy
=√2dxdy
So the original formula = ∫ (X & # 178; + Y & # 178;) √ 2dxdy (s represents the projection of the surface ∑ on the XY plane: X & # 178; + Y & # 178; = 4)
=√ 2 ∫ D θ∫ R & # 178; * RDR (polar coordinate transformation)
=√2π/2(2^4-0^4)
=8√2π.