【摘要】 文献[1]指出光滑性不是建立弧长计算公式的必要条件,并在导数x′(t),y′(t)可积的条件下建立了弧长计算公式.本文对可求长曲线弧长的计算问题进一步探讨,在黎曼(Riemann)可积条件下,给出有限维赋范线性空间上的曲线弧长计算公式.更多还原

【Abstract】 The paper [1] points out that smooth property is not the necessary condition of the calculation formula of arc length,and gives a calculation formula of arc length under the condition that derivativesx′(t),y′(t) are integrable.This paper further studies the calculating problem of arc length,and gives a calculation formula of arc length in the finite dimensional linear normed space under the condition that the curve is Riemann integrable.更多还原