Please show your work so that I'm able to understand how tosolve. Thank you.
Show several ways that the vector field F[X] = is not a gradient vector field. That is, prove that there cannot be a scalar function phi [X] so that phi [X] = F[X] or equivalently, d phi[X] = F[X] middot dX. Integrate F around the unit radius counterclockwise circle centered at the origin. Calculate Swirl[F[X]]. Sketch the vector field. Which of the methods (a)-(c) apply to the vector field W[X] = ?