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

question 197

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where S is the boundary surface of the region outside the sphere $\mathrm { x } ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$ and inside the ball $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4$ and $\mathbf { F } = e ^ { y ^ { 2 } } \mathbf { i } + \left( 5 y + e ^ { x ^ { 2 } } \right) \mathbf { j } + ( - 3 z + 2 x ) \mathbf { k }$ .

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Definitions:

Behavioral Economics

A field of economic research that examines how psychological, social, cognitive, and emotional factors affect economic decisions of individuals and institutions.

Brain Modularity

The concept that the human brain is composed of specialized modules or regions, each responsible for different functions or processes.

Availability Heuristic

A mental shortcut that relies on immediate examples that come to a person’s mind when evaluating a specific topic, concept, method, or decision.