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Find the length of the curve given by the parametric representation

  • Thread starter tamintl
  • Start date
  • #1
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Find the length of the curve given by the parametric representation....

Homework Statement


Calculate the length of the curve given by the parametric representation
r(t) = t2(cos t; sin t; cos 2t; sin 2t) for 1≤ t ≤+1:


Homework Equations





The Attempt at a Solution



I know that you need to assume: dx/dt ≥ 0 for α≤t≤β

Then you use the formula for 'L'

Imstruggling with the layout of the question.. Why are there semi-colons between the sin and cos terms?

If someone could explain this that would be great.

Regards as always.
 

Answers and Replies

  • #2
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There are probably semi-colons to distinguish between the four different dimensions. So x(t) = t^2 cos(t), y(t) = t^2 sint, etc.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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I presume you know that the length of the curve given by r(t), from t= a to t= b, is
[tex]\int_a^b ||r'(t)|| dt[/tex]
where r'(t) is the tangent vector and the || || is the length of that vector.
 

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