- #1

FrogPad

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Ok the question is:

[tex]\vec F(x,y)=<3xy,8y^2>\,=3xy\,\hat i + 8y^2\,\hat j[/tex]

[tex]C: y=8x^2[/tex]

Where [tex]C[/tex] joins [tex](0,0)\,,\,(1,8)[/tex]

Evaluate [tex]\int_{C} \vec F \cdot d\vec r [/tex]

I'm unsure how to evaluate this. I really do not want just an answer, I want to know how to solve it.

My first thought was to check if it is conservative then I can simply let [tex]\vec r(t) [/tex] be a line between the point. Or, (if conservative) I could use the fundamental theorem for line integrals. But:

[tex]\frac{dP}{dy} \neq \frac{dQ}{dx}[/tex]

...so it is not conservative.

My last idea is that I need to paramterize [tex]y=8x^2[/tex] and this is where I get kind of shaky as far as my abilities with vector calculus. (We just started this chapter). So any insight on this problem, or parameterizing functions would be awesome. Thanks in advance.

[tex]\vec F(x,y)=<3xy,8y^2>\,=3xy\,\hat i + 8y^2\,\hat j[/tex]

[tex]C: y=8x^2[/tex]

Where [tex]C[/tex] joins [tex](0,0)\,,\,(1,8)[/tex]

Evaluate [tex]\int_{C} \vec F \cdot d\vec r [/tex]

I'm unsure how to evaluate this. I really do not want just an answer, I want to know how to solve it.

My first thought was to check if it is conservative then I can simply let [tex]\vec r(t) [/tex] be a line between the point. Or, (if conservative) I could use the fundamental theorem for line integrals. But:

[tex]\frac{dP}{dy} \neq \frac{dQ}{dx}[/tex]

...so it is not conservative.

My last idea is that I need to paramterize [tex]y=8x^2[/tex] and this is where I get kind of shaky as far as my abilities with vector calculus. (We just started this chapter). So any insight on this problem, or parameterizing functions would be awesome. Thanks in advance.

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