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Homework Help: Integrate curve f ds Line Integrals

  1. Nov 8, 2012 #1
    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>

    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. jcsd
  3. Nov 9, 2012 #2


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    Gold Member

    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.
  4. Nov 9, 2012 #3
    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.

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