C为右半单位圆周
化为参数方程
x=cost y=sint t∈[-π/2,π/2]
∫C y² ds=∫[-π/2,π/2] sin²t√[(dx/dt)²+(dy/dt)²] dt
=∫[-π/2,π/2] sin²t dt
=∫[-π/2,π/2] (1-cos2t)/2 dt
=t/2-(sin2t)/4 | [-π/2,π/2]
=π/2