Ok, so let me start with the information that is given. I need to find the length of the curve.

x=t^3

y=3t^2/2

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:

y'=3t^2

x'=3t

then i square each of them, which gives:

9t^4

9t^2

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