1. to determine which field is conservative Calculuate curlF

If CurlF = 0 then F is conservative

2. To find V

1. Integrate the x component wrt x and add a fn h(y,z) instead of an integration constant

2. Differentiate the result wrt y and set it equal to the y component

Integrate this with respect to find h(y,z) and add on a fn g( z)

3. Differentiate this wrt to z snd set equal to the z- component

Integrat this and add it alll together

I'll illustrate with a simple example

F = yzi + (xz+2y)j +(xy+2z)k

V= xyz +h(y,z)

dV/dy = xz + dh/dy = xz + y

so dh/dy = y so h= y^2 + g(z)

V= xyz +y^2 +g(z)

dV/dz = xy + dg/dz = xy +2z

dg/dz = 2z so g = z^2

V= xyz + y^2 +z^2