Use Green's Theorem to Evaluate the Line Integral $\int _ { C } \left( e ^ { - x ^ { 2 } / 2 } - y \right) d x + \left( e ^ { - y ^ { 2 } / 2 } + x \right) d y$

question 79

Multiple Choice

Use Green's Theorem to evaluate the line integral $\int _ { C } \left( e ^ { - x ^ { 2 } / 2 } - y \right) d x + \left( e ^ { - y ^ { 2 } / 2 } + x \right) d y$ where $C$ is the boundary of the region lying between the graphs of the circle $x = 8 \cos \theta , y = 8 \sin \theta$ and the ellipse $x = 6 \cos \theta , y = 4 \sin \theta$ .

• A) \(120 \pi\)
• B) \(162 \pi\)
• C) \(172 \pi\)
• D) \(80 \pi\)
• E) \(91 \pi\)

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Definitions:

Situational Management

Situational management is an adaptive leadership approach that advocates for adjusting management style and strategies based on the specific circumstances and needs of the situation.

McGregor

Douglas McGregor developed the Theory X and Theory Y concept, representing two opposing perceptions of employee motivation and behavior.

Theory X

A management theory that assumes employees are inherently lazy and will avoid work if they can, suggesting the need for strict oversight and control.

Theory Y

A management concept that assumes employees are inherently motivated and enjoy their work duties, suggesting that the role of management is to develop the potential of employees and help them to achieve self-fulfillment.