## Problem on the arc length of a helix

Find the arc length of the helix $x(t) = \cos t, y(t) = \sin t, z(t) = t$ traced from $t=1$ to $t=2$.
• ## Solution

Recall that
We identify $a=1$ and $b=2$ and need to compute the speed as a function of $t$.
Thus, the arc length swept between $t=1$ and $t=2$ is $$s = \int_1^2 \sqrt{2} dt = \sqrt{2}.$$