Determine Whether or Not $\mathbf { F } ( x , y ) = \left( x ^ { 2 } + y \right) \mathbf { i } + \left( y ^ { 2 } + x \right) \mathbf { j }$

Essay

Determine whether or not $\mathbf { F } ( x , y ) = \left( x ^ { 2 } + y \right) \mathbf { i } + \left( y ^ { 2 } + x \right) \mathbf { j }$ is a conservative vector field. If it is, find a function f such that $\mathbf { F } = \nabla f$