Calculate the Flux of the Field F Across the Closed $\mathbf { F } = \mathrm { e } ^ { 5 \mathrm { x } _ { \mathrm { i } } + \mathrm { e } ^ { 2 } \mathrm { y } } \mathrm { j }$

question 19

Multiple Choice

Calculate the flux of the field F across the closed plane curve C.
- $\mathbf { F } = \mathrm { e } ^ { 5 \mathrm { x } _ { \mathrm { i } } + \mathrm { e } ^ { 2 } \mathrm { y } } \mathrm { j }$ ; the curve $\mathrm { C }$ is the closed counterclockwise path around the triangle with vertices at $( 0,0 ) , ( 5,0 )$ , and $( 0,1 )$

• A) \(\frac { 1 } { 5 } e ^ { 25 } \left( 1 - e ^ { - 5 } \right) + \frac { 5 } { 2 } \left( e ^ { 2 } - 1 \right) + 6\)
• B) \(\frac { 1 } { 25 } \mathrm { e } ^ { 25 } \left( 1 - \mathrm { e } ^ { - 25 } \right) + \frac { 5 } { 2 } \left( \mathrm { e } ^ { 2 } - 1 \right) - 6\)
• C) \(\frac { 1 } { 5 } \mathrm { e } ^ { 25 } \left( \mathrm { e } ^ { - 5 } - 1 \right) + \frac { 5 } { 2 } \left( 1 - \mathrm { e } ^ { 2 } \right) - 6\)
• D) 0

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Definitions:

Six Sigma

Systems approach to quality management providing training for employees and managers in statistical analysis, project management, and problem-solving methods to reduce the defect rate of products.

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A state or condition where a product, service, or process is free of flaws, errors, or deficiencies, meeting all specified requirements.

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A methodological approach aimed at improving processes by identifying and eliminating defects.

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