Use the Divergence Theorem to Find the Flux of the Vector

question 1

Essay

Use the Divergence Theorem to find the flux of the vector field ${ \vec { F } } = \left( y ^ { 2 } x - 3 z ^ { 2 } y \right) \vec { i } + \left( z ^ { 2 } y + z x ^ { 3 } \right) \vec { j } + \left( x ^ { 2 } z + y x \right) \vec { k }$ through the sphere x² + y² + z² = $1$ .

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Definitions:

Polygyny

A form of marriage in which a man is allowed to have more than one wife at the same time.

Polyandry

A form of marriage in which a woman has two or more husbands at the same time.

Monogamy

One person is married exclusively to another person.

Exclusively Married

A state or condition in which individuals are married and do not engage in marital relationships with anyone else.