Using Green's Theorem, Compute the Counterclockwise Circulation of F Around

question 96

Multiple Choice

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
- $\mathbf { F } = \left( x - e ^ { \mathrm { x } } \cos y \right) \mathbf { i } + \left( x + \mathrm { e } ^ { \mathrm { x } } \sin \mathrm { y } \right) \mathbf { j } ; \mathrm { C }$ is the lobe of the lemniscate $\mathrm { r } ^ { 2 } = \sin 2 \theta$ that lies in the first quadrant.

• A) 0
• B) \(\frac { 1 } { 2 }\)
• C) 1
• D) \(\frac { 1 } { 4 }\)

---

Definitions:

Celibacy

The state of abstaining from marriage and sexual relations, often for religious or spiritual reasons.

Lucrative Job

A job or employment that is highly profitable and provides a significant financial return or benefit.

Monogamy

A relationship model where an individual has only one partner during their lifetime or at any one time.

Polygyny

A form of marriage in which one man is married to multiple women at the same time; it is the most common form of polygamy.