az/ax=2x,az/ay=2y
dS=根号(1+(az/ax)²+(az/ay)²)dxdy
=根号(1+4x²+4y²)dxdy
∫∫ dS
=∫∫ 根号(1+4x²+4y²)dxdy (D:x²+y²≤1)
D
=∫∫ 根号(1+4p²)pdpdθ
=∫(0,2π)dθ∫(0,1) 根号(1+4p²)pdp
=2π·1/8∫ (0,1)根号(1+4p²)d(1+4p²)
=π/4 ·2/3 (1+4p²)^(3/2)|(0,1)
=π/6 (5^(3/2)-1)
=π/6 (5根号5 -1)