How can you tell if a vector field is conservative?

In my calculus class we've started going over vector fields and line integrals, but I'm confused as to how you go about deciding whether or not a vector field is conservative, or what it even means for a vector field to be conservative in the first place. Any help would be great.|||If you have W= INT_C (F dot dR ) that it is





W= INT _C (Fx dx + Fy dy ) between Point P1 and P2 on the curve C





If you can find a Function G such as Nabla G =(Fx dx + Fy dy ) , then





W= INT_C Nabla G and the solution willl be ( G(P2) - G(P1) ) and you can say that field of vector F is conservative , because depends of end point (P2) and the initial point P1 , it doesn麓t depend of curve C .- If it is conservative the ROTOR of F =0 ( ROT F =0)





Then you can find G ,if ROT F=0 , since


dG = DG/dx dx+ DG/dy dy = Fx dx +Fy dy





DG/dx= Fx


DG/dy= Fy





G(x,y) = INT Fx dx + g(y)


DG/dy = d/dy (INT Fx dx + g(y)) = Fy


From this you find g(y) and add a constant C


plug and you get G(x,y) .-