Consider the parametric equation <mstyle displaystyle="true"> x = 9

Frederick Kramer

Frederick Kramer

Answered question

2022-07-13

Consider the parametric equation x = 9 ( cos t + t sin t ) and y = 9 ( sin t - t cos t ) , What is the length of the curve for t = 0 to t = 3 π 10 ?

Answer & Explanation

escampetaq5

escampetaq5

Beginner2022-07-14Added 12 answers

Step 1
We have
{ d x d t = 9 t cos t d y d t = 9 t sin t
and
d s d t = ( d x d t ) 2 + ( d y d t ) 2 = 9 t
Step 2
then
s = t = 0 t = 3 π 10 9 t d t = 9 2 ( 3 π 10 ) 2

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