# Find the length of the curve given by the parametric representation

1. Nov 20, 2011

### tamintl

Find the length of the curve given by the parametric representation....

1. The problem statement, all variables and given/known data
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:

2. Relevant equations

3. 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.

2. Nov 20, 2011

### murmillo

Re: Find the length of the curve given by the parametric representation....

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. Nov 21, 2011

### HallsofIvy

Staff Emeritus
Re: Find the length of the curve given by the parametric representation....

I presume you know that the length of the curve given by r(t), from t= a to t= b, is
$$\int_a^b ||r'(t)|| dt$$
where r'(t) is the tangent vector and the || || is the length of that vector.