Let $\vec{F}$ And $\vec { G }$ Be Two 2-Dimensional Fields, Where $\vec{F}=3 x \vec{i}+5 y \vec{j}$

question 66

Short Answer

Let $\vec{F}$ and $\vec { G }$ be two 2-dimensional fields, where $\vec{F}=3 x \vec{i}+5 y \vec{j}$ and $\vec { G } = 3 y \vec { i } + 5 x \vec { j }$ Let C₁ be the circle with center (2, 2)and radius 1 oriented counterclockwise.
Let C₂ be the path consisting of the straight line segments from (0, 4)to (0, 1)and from (0, 1)to (3, 1).
Find the line integral $\int_{c_{2}} \vec{F} \cdot d \vec{r}$ Use "pi" to represent $\pi$ if necessary.

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Definitions:

Unipolar Depression

A form of depression where the individual experiences persistent low mood and a lack of interest or pleasure in activities, without the manic or hypomanic episodes found in bipolar disorder.

Dysregulation

An impaired ability to regulate emotional responses or processes, often leading to psychological distress.

Severe Unipolar Depression

A major depressive disorder characterized by a persistent and profound sadness or lack of interest in external stimuli, without the manic episodes seen in bipolar disorder.

Learned Helplessness

a condition in which a person suffers from a sense of powerlessness, arising from a traumatic event or persistent failure to succeed, leading to decreased motivation and depression.