A curtate cycloid is defined by the equations x = 2t - sin t and y = t - cos t. If I walk along the cycloid, how far will I walk in 10 seconds?

Answer 1

ds^2 = dx^2+dy^2
= (2-cos t)^2 + (1+sin t)^2
= 4 - 4cost + cos^2 t + 1 + 2sint + sin^2 t
= 6 - 4cost + 2sint

The problem is, that this results in an elliptic integral, which is not usual in low-level calculus classes