Find the arclength of the curve r ( t ) =&lt; − 9 sin ⁡ t , 2 t , − 9 cos ⁡ t &gt; , − 8 ≤ t ≤ 8

Question

Find the arclength of the curve   r  (  t  )  =&amp;lt;  −  9  sin  ⁡  t  ,  2  t  ,  −  9  cos  ⁡  t  &amp;gt;  ,  −  8  ≤  t  ≤  8

Milton Gilmore · Accepted Answer

We have  r  (  t  )  =&amp;lt;  −  9  sin  ⁡  t  ,  2  t  ,  −  9  cos  ⁡  t  &amp;gt;  ,  −  8  ≤  t  ≤  8        r    ′    (  t  )  =&amp;lt;  −  9  cos  ⁡  t  ,  2  ,  9  sin  ⁡  t  &amp;gt;        |        r    ′    (  t  )      |    =      (    −    9    cos    ⁡    t          )      2        +          2      2        +    (    9    sin    ⁡    t          )      2          =      81          cos      2        ⁡    t    +    4    +    81          sin      2        ⁡    t      =      81    +    4          |        r    ′    (  t  )      |    =      85  Arc length =   16      85

Find the arclength of the curve r(t) = (-9 sin t, 2t, -9 cos t), -8<= t<=8

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