Mathematics

Problem

Let

g

be differentiable on

[0,2]

. The limit of Riemann sums

\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}\sqrt{1+\bigl(g'(x_{i})\bigr)^{2}}\,\Delta x_{i}

approximates the length of the graph of

g

on this interval. Write this limit as an equivalent definite integral.