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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }

question 49

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Evaluate SFdS\iint _ { S } \mathbf { F } \cdot d \mathbf { S } , where F=(x,y,z) =yj+zk\mathbf { F } = ( x , y , z ) = y \mathbf { j } + z \mathbf { k } and S is the cube bounded by x=±1,y=±1,z=±1x = \pm 1 , \quad y = \pm 1 , \quad z = \pm 1 .


Definitions:

Mature Pollen Grain

The haploid male gametophyte phase of plants that contains the cells that will fertilize female ovules, enabling sexual reproduction.

Male Gametophyte

The haploid stage in the life cycle of plants that produces the male gametes or sperm cells.

Diploid Sporophyte

The phase in the life cycle of plants and some algae that has two sets of chromosomes and typically produces spores.

Angiosperm Life Cycle

A reproductive cycle that includes both asexual and sexual phases, characterized by the development of flowers and formation of seeds within an enclosed ovary.

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