The arc length l of a curve given parametrically by

(x(t), y(t)) for a = t = b
is given by the formula

l = b (x '(t))2 + (y '(t))2
dt

a

a path of a point on the edge of a rolling circle of radius r is a cycloid, given by

x(t) = r (t - sin t),

y(t) = r (1 - cos t),
where t is the angle (in radians) the circle has rotated.

find the length l of one "arch" of this cycloid, that is, find the distance traveled by a small stone stuck in the tread of a tire of radius r during one revolution of the rolling tire.