Clothoid curve is described by $rl=A^2$, where $r$ is turning radius and $l$ is length from the origin. (This definition is very intuitive to understand for me)
Also it's known that the coordinate $(x,y)$ is described as following.
$x(l) = \int_0^l \cos(s^2)ds$, $y(l) = \int_0^l \sin(s^2)ds$
But how can I derive these equations from $rl=A^2$ ?
I searched a hint but I wasn't able to get, probably because it's too obvious for other people. Thanks.