I'm reading this.
The relevant definitions are that of parametrized curve which is at the beginning of page 1 and the definition of arclength of a curve, which is in the first half of page 6.
Also the author mentions the helix at the bottom of page 3.
On exercise $1.1.2.$ (page 8) I'm asked to find the arc length of the helix:
$\alpha (t)=(a\cos (t), a\sin (t), bt)$, but the author don't say what the domain of $\alpha$ is.
How am I supposed to go about this?
Usually when the domain isn't specified isn't the reader supposed to assume the domain is a maximal set? In that case the domain would be $\Bbb R$ and the arc length wouldn't be defined as the integral wouldn't be finite.