Vector field problem

**pdnhan** · May 14th 2010, 05:31 AM

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

**General** · May 14th 2010, 05:32 AM

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

**pdnhan** · May 14th 2010, 05:34 AM

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

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