Ok, so let me start with the information that is given. I need to find the length of the curve.
0≤ t ≥ square root (3)
So that's the information that is given. Now I believe the correct equation to use is this Mathwords: Arc Length of a Curve (parametric form)
(sorry for the link, but i have no idea how to type something like that)
Ok. so first I take the derivative of each of the functions, which gives:
then i square each of them, which gives:
So putting that into the fuction, it gives
(9t^4 +9t^2)^ 1/2
then taking the integral of that, i get
2(9t^4 +9t^2)^ 3/2/ 3(36t^3 +18t)
and evalutating at square root 3, i get 3.42857....
but the answer in the book says 7.
can anyone help me out here and point out what i did wrong? i may be way off, as i'm just learning this, but i need to know how to do this.
oh for the love of god none of my notation worked. i will edit this and make it better.
ok, that should be be better