Fundamental Theorem Line Integrals

[mammothrob]

So here im trying to revcover a potential function to evaluate the integral.

\(\displaystyle \int\limits_{(1,2,1)}^{(2,1,1)} {(2x\ln y - yz)dx + (\frac{x}
{{yz}} - xz)dy - (xy)dz}\)

so i conside the the dx portion as fx and partialy integrate with respect to x

\(\displaystyle 2xlyy - yz = x^2 \ln y - yzx + g(y,z)\)

I then I partially derive with respect to y

\(\displaystyle \frac{{x^2 }}
{y} - zx + g_y (y,z)\)

my problem is that the my potential function is not the gradiat of the original. Am I doing this right, or can this one not be integrated with the fundamental theorem of line integrals?

Any help is much appreciated.
Rob

 

[Unco]

\(\displaystyle \mbox{F(x,y,z) = (2x\ln y - yz, \frac{x}{yz} - xz, -xy)}\) is not a conservative field as you can quickly check by testing its curl, so the integral is not independent of path.

 

[mammothrob]

Thanks... I have my calc III final tomorrow and that was an example on our review handout. It was freaking me out a little.
...............Back to studying.................