# Thread: vector field and curl

1. ## potential vector

The vector field F(x,y)=( $y^2$ +cosx i )+ 2xy j in the plane is conservative.

can I conclude this statement is right if I found the potential f(x,y)=x $y^2$ + sinx ?

2. Originally Posted by yzc717
The vector field F(x,y)=( $y^2$ +cosx i )+ 2xy j in the plane is conservative.

can I conclude this statement is right if I found the potential f(x,y)=x $y^2$ + sinx ?
Yes.

$\nabla \times F = 0 \Longleftrightarrow F = \nabla f$