The arc length of the curve defined by the graph of y = f ( x ) , a ≤ x ≤ b , {\displaystyle y=f(x),\,a\leq x\leq b,} is L = ∫ a b 1 + [ f ′ ( x ) ] 2 d x . {\displaystyle L=\int _{a}^{b}{\sqrt {1+[f'(x)]^{2}}}\,dx.}
![{\displaystyle L=\int _{a}^{b}{\sqrt {1+[f'(x)]^{2}}}\,dx.}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/01f9c77e776ed09477e79963fa5383c0d3cd7579)