How to get the length of a curve that doesn't have an equation?

Question

is there any way of finding out the length of a curve that doesn't have an equation but is instead plotted on a graph?

Answer 1

To get a very first approximation, start on the left of the curve and pick the coordinates of the first point $(x_1,y_1)$. Following the curve, take the coordinates of the next point $(x_2,y_2)$ and so on up to the last point $(x_n,y_n)$.

So, the approximate length will be $$L=\sum_{i=1}^{n-1} \sqrt{(x_{i+1}-x_i)^2+(y_{i+1}-y_i)^2}$$