Using Green's Theorem, Compute the Counterclockwise Circulation of F Around $\mathbf { F } = \sin 5 y \mathbf { i } + \cos 7 x \mathbf { j } ; \mathrm { C }$

question 207

Multiple Choice

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
- $\mathbf { F } = \sin 5 y \mathbf { i } + \cos 7 x \mathbf { j } ; \mathrm { C }$ is the rectangle with vertices at $( 0,0 ) , \left( \frac { \pi } { 7 } , 0 \right) , \left( \frac { \pi } { 7 } , \frac { \pi } { 5 } \right)$ , and $\left( 0 , \frac { \pi } { 5 } \right)$

• A) \(- \frac { 2 } { 5 } \pi\)
• B) \(- \frac { 4 } { 5 } \pi\)
• C) \(\frac { 2 } { 5 } \pi\)
• D) 0

---

Definitions:

Psychiatrist

A medical doctor specializing in the diagnosis, treatment, and prevention of mental health and emotional disorders, capable of prescribing medication.

Theoretically Diverse

Characterized by a wide range of theories or ideas in a particular field or subject, reflecting a broad spectrum of viewpoints.

Empirical Observations

Information gathered directly through the senses or instrumentation, forming the basis for scientific inquiry and evidence.

Psychology

The systematic exploration of human mind and its operations, particularly those influencing behavior in specific situations.