> See also: > - Reference # Arc Length Formula Consider a function $f$ where $f'$ is continuous on $[a,b]$. We define the length of the curve $y=f(x)$ from the point $(a,f(a))$ to the point $(b,f(b))$ this way: $L=\int^{b}_{a}\sqrt{1+[f'(x)]^2}dx$ ![[Pasted image 20240122233212.png|300]] can be thought of as a summation of distance formulas