Our first objective is to define what we mean by thelength(also called thearc length)ofa plane curvey=f(x)over an interval[a, b](Figure 6.4.1). Once that is done we will beable to focus on the problem of computing arc lengths. To avoid some complications thatwould otherwise occur, we will impose the requirement thatfbe continuous on[a, b], inwhich case we will say thaty=f(x)is asmooth curveon[a, b]or thatfis asmoothfunctionon[a, b]