(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Compute ∫f ds for [tex]f(x,y)=\frac {y^3}{x^7}[/tex] [tex]y=\frac {x^4}{4}[/tex] for [itex]1≤x≤2[/itex]

2. Relevant equations

∫f ds= ∫f(c(t))||c'(t)||

||c'(t)|| is the magnitude of ∇c'(t)

3. The attempt at a solution

From this... I gathered the following, by saying x=t

[tex]c(t)= <t,\frac {t^4}{4}>[/tex]

[itex]c'(t)= <1, t^3>[/itex]

That gave me a magnitude of [tex]\sqrt{1+t^6}[/tex]

so now I get that ∫f ds... through plugging in the magnitude and c(t) in the integral... this

[itex]∫\frac{t^5 \sqrt{1+t^6}}{64}[/itex] where [itex] x=t\, and\, 1≤t≤2 [/itex]

This is the part where I'm particularly stuck... am I missing a step or did I make a math error??? How do I integrate this?

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# Homework Help: Tricky to 2 variable line/path integral

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