razroz
Evaluate the line integral f(x,y)ds along the parametric curve: f(x,y)=3x+4y^2;x=2t1, y=t+5, 1(<or=) t (<or=) 2



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amistre64
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\[ds =\sqrt{(x')^2+(y')^2}\]

amistre64
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well, in this case i spose fx and fy for partials

razroz
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so i take the partial of both x and y with respect to t and plus that under a square root next to the function f(x,y) and integrate?

amistre64
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yes, but dont forget to replace x and y with their t equations within f
f(x,y)=3x+4y^2;x=2t1, y=t+5
f(t)=3(2t1)+4(t+5)^2

amistre64
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or am i mixing things up?

Algebraic!
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ds = v(t) dt

amistre64
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im mixing a vector feild in with this i believe

razroz
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no i believe you are right, let me write it out real quick

Algebraic!
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you're fine @amistre64

razroz
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so i would just get a sqrt(5) from the ds, then the function would read integral of (3(2t1)+4(t+5)^2)dt (times the sqrt(5))?

amistre64
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..... thnx ;)

amistre64
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yep, but put the sqrt5 inside the integral

Algebraic!
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yes correct, @razroz

razroz
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thank you so much

amistre64
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good luck ;)