I'm doing a vector arclength problem, and have gotten to the part where I have $\int | r'(t) | dt. $
Both $r(t)$ and $r'(t)$ are unknown functions, though I do know that $0 \leq r(t)$ for $a ≤ t ≤ b$.
I now that I would normally integrate by dividing the integral into two parts such as when I'm given a definite integral, but since $r'(t)$ can very well be negative at any point, I'm not sure currently? It's probably something stupid that I'm forgetting anyways, but thanks anyways.