Homework Help: Integrate curve f ds Line Integrals

1. Nov 8, 2012

Unart

1. The problem statement, all variables and given/known data
Compute ∫f ds for f(x,y)= √(1+9xy), y=x^3 for 0≤x≤1
2. Relevant equations

∫f ds= ∫f(c(t))||c'(t)||

||c'(t)|| is the magnitude of ∇c'(t)

3. The attempt at a solution

So, with this equation y=x^3 ... I got the that c(t)= <t,t^3>
c'(t)=<1,3t^2>

I know that from the equation y=x^3... x=t=0 and 1... I don't know how to get the magnitude of such equation. They the lower and upper limit.

Another thing is I cannot for the life of me figure out how to take the anti-derivative of √(1+9xy)... which by the time I change to t it would be √(1+9t^4)...

Of course if I'm approaching this the wrong way please, tell me what I'm doing wrong. Please let me know if it isn't clear enough.

2. Nov 9, 2012

haruspex

Do you mean ||c'(t)|| is the magnitude of ∇c(t)?
So ||c'(t)|| = √(1+9t4), yes?
Yes, but after you multiply that by ||c'(t)|| it will look a lot nicer.

3. Nov 9, 2012

Unart

No joke.... thanks to you. It cleared up a whole lot of dark and dreary confusion. I was plugging the number into the Magnitude equation and getting just a number for the magnitude. I didn't know that you just took the derivative as and used the magnitude equation from that.

THANKYOU!!!
I posted another question and the past and began to worry if my wording or something was off.