Exercise · ZW-ARC-LENGTH-001 · ★☆☆ Basic
Find the length of \(\mathbf r(t)=\langle3t,4t\rangle\) for \(0\le t\le2\).
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- C. \(10\)
Explanation
\(\mathbf r'(t)=\langle3,4\rangle\), with \(|\mathbf r'|=5\). Then \(L=\int_0^2 5\,dt=10\).
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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