How does the formula for length of a graph relate to that of parametric description? So I know how to solve for the length of a regular graph and for a parametric description.

Regular graph length formula:
$$L = \int_{x=a}^{x=b}\sqrt[]{1 + (f'(x))^2} \,\,\,dx$$

Parametric description length formula:
$$\int_{t = a}^{t=b} \sqrt[]{(x'(t))^2+(y'(t))^2} \,\,\,\,dt$$

The form of these two are so radically different that I can't see how one relates to the other. The parametric description uses the form for path velocity but I don't understand why..
If more elaboration is needed, please ask. I'll supply.
Highly appreciated,
-Bowser

They are radically similar ;) you forgot the integral in your first formula (edit: I see you fixed it now)
Notice that you can parametrize the graph of $f$ by $$(t, f(t))$$ Now use the second formula, you will get the first!
