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

question 214

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 $\mathbf { F } = \nabla f$

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Definitions:

Ammonia

A compound of nitrogen and hydrogen (NH3) that is a byproduct of the metabolism of animals and is used in various industrial processes.

Metanephridial Organs

Metanephridial organs are excretory structures in some invertebrates, including annelids, that filter fluid directly from the animal's body cavity.

Mollusks

Invertebrates with a soft body, often protected by a hard shell, belonging to the phylum Mollusca, which includes snails, clams, and squids.

Common

Referring to something that is usual, typical, or shared among multiple entities or individuals.