Sketch the curve and find its arc length
r(t) = (cos π t, sin π t, cos 4 π t), 0 ≤ t ≤ 2
It might help to note that, for all t, $\displaystyle x^2+ y^2= cos^2(\pi t)+sin^2(\pi t)= 1$ so the projection into the xy- plane is a circle. How does z vary?
The arclength is, of course $\displaystyle \int_0^2\sqrt{\left(\frac{d cos(\pi t)}{dt}\right)^2+ \left(\frac{d sin(\pi t)}{dt}\right)^2+ \left(\frac{d cos(4\pi t)}{dt}\right)^2} dt$.
Can you do that?