Calculate the Flow in the Field F Along the Path $\mathbf { F } = \mathrm { e } ^ { 2 } \mathrm { i } + \frac { 1 } { \mathrm { y } } \mathrm { j } + 2 \mathbf { k } , \mathrm { C }$

question 74

Multiple Choice

Calculate the flow in the field F along the path C.
- $\mathbf { F } = \mathrm { e } ^ { 2 } \mathrm { i } + \frac { 1 } { \mathrm { y } } \mathrm { j } + 2 \mathbf { k } , \mathrm { C }$ is the curve $\mathbf { r } ( \mathrm { t } ) = 4 \mathrm { t } ^ { 2 } \mathrm { i } + 5 \mathrm { tj } + ( - 8 - 2 \mathrm { t } ) \mathbf { k } , 1 \leq \mathrm { t } \leq 3$

• A) \(4 \left( \mathrm { e } ^ { 225 } - \mathrm { e } ^ { 25 } \right) + \ln 3 - 8\)
• B) \(\frac { 8 } { 25 } \left( \mathrm { e } ^ { 225 } - \mathrm { e } ^ { 25 } \right) + \ln 3 - 8\)
• C) \(\frac { 4 } { 25 } \left( e ^ { 225 } - e ^ { 25 } \right) + \ln 3 - 8\)
• D) \(\frac { 4 } { 25 } \left( \mathrm { e } ^ { 225 } - \mathrm { e } ^ { 25 } \right) + \ln 3 + 8\)

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Definitions:

Psychoanalytic Theorist

An expert in the field of psychoanalysis who studies unconscious factors that influence behavior and mental processes.

Erikson

A developmental psychologist named Erik Erikson known for his theory on the psychosocial development of humans through eight stages from infancy to late adulthood.

Classical Conditioning

A learning process that occurs when two stimuli are repeatedly paired; a response that is at first elicited by the second stimulus is eventually elicited by the first stimulus alone.

Behaviorist Perspective

A theory in psychology that focuses on observing and controlling behavior, emphasizing the effects of external stimuli on observable behaviors and discounting thoughts and feelings.