(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Integrate curve f ds Line Integrals

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