Find the length of the curve given by the parametric representation

[tamintl]

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.

 

[murmillo]

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.

 

[HallsofIvy]

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.