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