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

Zackary Diaz 2022-11-20 Answered
Find the arclength of the curve r ( t ) =< 9 sin t , 2 t , 9 cos t > , 8 t 8
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Answers (1)

Milton Gilmore
Answered 2022-11-21 Author has 20 answers
We have
r ( t ) =< 9 sin t , 2 t , 9 cos t > , 8 t 8 r ( t ) =< 9 cos t , 2 , 9 sin t > | 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
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