曲面2z=x^2+y^2被柱面(x^2+y^2)^2=x^2-y^2所截下部分的曲面

柱面(x^2+y^2)^2=x^2-y^2化成极坐标方程是r^2=cos2θ.
即r=√cos2θ.θ的范围是[-π/4,π/4]∪[3π/4,5π/4]
S=∫∫dS=∫∫√[1+(z'x)^2+(z'y)^2]dxdy=∫∫√[1+x^2+y^2]dxdy=∫∫√[(1+r^2)] rdrdθ
=4∫(0->π/4)dθ∫(0->√cos2θ)√[(1+r^2)] rdr
=20/9-π/3