1. ## Vector field problem

Consider the vector field:
$\displaystyle f(x,y,z)=(2xy^2-2y^2,2y-4xy+2x^2y,1)$
and let C be any smooth curve joining the origin to the point (1,1,1)
(a) Show that f is conservative by constructing a scalar patential $\displaystyle \phi$ such that $\displaystyle f = \nabla \phi$
(b) Hence determine $\displaystyle \int_{C} = f.dr$ without doing an integral
(c) Confirm your answer by direct integration using any convenient choice of C.