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Find the arc length of the given curve on the specified interval.

(6 cos(t), 6 sin(t), t), for 0 ≤ t ≤ 2π

User Hnguyen
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1 Answer

6 votes

Answer:

Explanation:

Given that


r(t) = (6cost, 6sint, t), 0\leq t\leq 2\pi\\r'(t) = (-6sint, 6cost, 1),\\||r'(t)||=√((-6sint)^2 +(6cost)^2+1) =√(37)

Hence arc length =
\int\limits^a_b  \, dt

Here a = 0 b = 2pi and r'(t) = sqrt 37

Hence integrate to get


\int\limits^(2\pi)  _0  {√(37) } \, dt\\ =√(37) (t)\\=2\pi√(37)

User Margi
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