Exercise · ZW-ARC-LENGTH-003 · ★☆☆ Basic
Find the length of \(\mathbf r(t)=\langle t,2t,2t\rangle\) for \(0\le t\le3\).
Choose one option.
Show answer
- D. \(9\)
Explanation
\(|\mathbf r'|=\sqrt{1+4+4}=3\), so \(L=\int_0^3 3\,dt=9\).
Review the concept: Arc length
The arc length of a parametric curve \(\mathbf r(t)\), with \(a\le t\le b\), is the total distance \(L\) traveled along it, measured along the curve itself.
\[L=\int_a^b\lvert\mathbf r'(t)\rvert\,dt\]
More practice problems: arc length
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