Question

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

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

Answer 1

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)`