 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/ia/paper-3/3c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-07

r^{'} = e^{t} (2, - sin t - cos t, cos t - sin t)

. The squared speed is

4 e^{2 t}

, so the arc length is

\int_{0}^{1} ∣ r^{'} ∣ d t = 2 (e - 1) .

The speed never vanishes, so this is a regular curve throughout its parameter range.

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