Line Integrals / Conservative Vector Fields

[randomguy123]

Homework Statement

$$F = < z^2/x, z^2/y, 2zlog(xy)>$$
$$F = \nabla f$$, where $$f = z^2log(xy)$$

Homework Equations

Evaluate $$\int F \cdot ds$$ for any path c from $$P = (1/2, 4, 2)$$ to $$Q = (2, 3, 3)$$ contained in the region $$x > 0, y > 0, z > 0$$

Why is it necessary to specify that the path lie in the region where $$x, y, z$$ are positive?

The Attempt at a Solution

I did $$f(2,3,3) - f(1/2,4,2)$$ to get $$9*log(6) - 4*log(2)$$

I don't really have an idea of how to answer the second question. Does it have to do with closed paths?

 

[latentcorpse]

think about the domain of the log function.

 

[lanedance]

or the first 2 elements of F