解：见下图：
微元dS=(1/2)[(2/sinθ)^2-1]dθ+(1/2){[2/sin(π/2-θ)]^2-1}dθ; 积分区间[0,π/4]和[π/4,π/2]
S=(1/2)∫(0,π/4)[(2/sinθ)^2-1]dθ+(1/2)∫(π/4,π/2)[2/sin(π/2-θ)]^2-1}dθ
如图所示
