Need help with Parametrization (just a quick question )

[goku900]

I'm studying flux and circulation but I just need help with this parametrization

on the parabola y = 2x^2 from (0; 0) to (2; 8)

How do I parametrize this to get r(t) = < 2t, 8t^2> That's the answer the book has but idk how to get.

I have the vector <t, 2t^2 > but not sure where to work from there

 

[pka]

on the parabola y = 2x^2 from (0; 0) to (2; 8)
How do I parametrize this to get r(t) = < 2t, 8t^2> That's the answer the book has but idk how to get.
I have the vector <t, 2t^2 > but not sure where to work from there

If we use \(\displaystyle \rho(t)=(t,2t^2)\) then \(\displaystyle 0\le t\le 2\).

However, if we use \(\displaystyle \rho(t)=(2t,8t^2)\) then \(\displaystyle 0\le t\le 1\).

Some authors insist that the parameter be \(\displaystyle \in[0,1]\). I have no idea why that is.