A simple method to find the potential of a(adsbygoogle = window.adsbygoogle || []).push({}); conservativevector field defined on a domain ##D## is to calculate the integral

$$U(x,y,z)=\int_{\gamma} F \cdot ds$$

On a curve ##\gamma## that is made of, that start from a chosen point ##(x_0,y_0,z_0)##.segments parallel to the coordinate axes

I would like to know what are precisely the conditions that ##D## must satisfy to use this method. ##D## should be made in such way that "any point can be connected to ##(x_0,y_0,z_0)## with, indeed, a segment parallel to the coordinate axes".

But what arethe sufficient mathematical conditions for $D$ in order to have this property?**

I would say that it surely has to be connected, but that seems not to be enough. For example taking

$$D= \{ (x,y) : y>x-1\} \,\,\,\, \,\,\,\,\,(x_0,y_0)=(0,0)$$

##D## is connected but I do not think that any point can be connected to ##(0,0)## via a segment parallel to the coordinate axes.

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# I Find potential integrating on segments parallel to axes

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