Find the Flux Of Across the Surface of the Solid $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1$

question 111

Short Answer

Find the flux of $\mathbf { F } ( x , y , z ) = \left( x ^ { 2 } z + \frac { 1 } { \ln ( y + 3 ) } \right) \mathbf { i } + \left( x y z + \frac { 1 } { ( y + 3 ) } \right) \mathbf { j } + \left( x z ^ { 2 } + \frac { z } { ( y + 3 ) ^ { 2 } } \right) \mathbf { k }$ across the surface of the solid $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 1$ .

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Definitions:

Cephalization

The concentration of nerve tissue and sensory organs at the anterior end of an organism, leading to the formation of a head region.

Bilateral Symmetry

A condition where an organism can be divided into two identical halves along a single plane.

Setae

Bristlelike structures that aid in annelid locomotion.

Protostomes

A group of animals characterized by developmental patterns where the mouth develops from the primary embryonic opening.