Show that x is the Arc-length Parameter for C

Question

I'm given a function for the plane of a curve in terms of $c(t)=(x(t),y(t))$

$x(t)$ and $y(t)$ are both definite integrals in terms of $\tau$ (not $t$).

I need to "Show rigorously that $t$ is the arc-length parameter for $c$"

I'm not looking for the full answer, but I don't understand the question itself. What is it actually asking for?

I understand how to parameterise the curve, but I don't know if that's what's being asked.

Thanks for your help.

Answer 1

You have not shown us these integrals, but if they look like $$x(t):=\int_0^t a(\tau)\>d\tau,\qquad y(t):=\int_0^t b(\tau)\>d\tau$$ with given continuous functions $a(\cdot)$, $b(\cdot)$ then the test is easy: Try to compute the arc length of this curve using the formula you know.