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:

Peak Workloads

Periods during which the volume of work or demand is at its highest, often requiring extra resources or effort.

Self-Actualizing

The realization or fulfillment of one's talents and potentialities, especially considered as a drive or need present in everyone.

Self-Determination Theory

A theory of motivation that emphasizes the role of intrinsic and extrinsic motivation in driving human behavior and the importance of autonomy, competence, and relatedness.

External Rewards

Incentives or benefits provided by external sources, such as money, praise, or recognition, that motivate individuals to perform certain actions.