曲线积分计算∮LxdL,其中L是由y=x与y=x^2所围城区域的整个边界

L1：y = x、dy/dx = 1、ds = √[1 + (dy/dx)^2] dx = √2 dx
L2：y = x^2、dy/dx = 2x、ds = √[1 + (dy/dx)^2] dx = √(1 + 4x^2) dx
∮ x ds
= ∫L1 x ds + ∫L2 x ds
= ∫(0→1) x √[1 + (dy/dx)^2] dx + ∫(0→1) x √[1 + (dy/dx)^2] dx
= ∫(0→1) x * √2 dx + ∫(0→1) x√(1 + 4x^2) dx
= 1/√2 + (1/12)(5√5 - 1)
= (6√2 + 5√5 - 1)/12