Thread: Vector field problem

1. Vector field problem

Consider the vector field:
$f(x,y,z)=(2xy^2-2y^2,2y-4xy+2x^2y,1)$
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 $\phi$ such that $f = \nabla \phi$
(b) Hence determine $\int_{C} = f.dr$ without doing an integral
(c) Confirm your answer by direct integration using any convenient choice of C.
Please help

2. Did you try anything ??
Do you know the steps for solving the first part ??

3. sorry about that, I know (a) and (c), needing help with (b), thanks