Find the Value of the Line Integral $\int_{c} \mathbf{F} \cdot d \mathbf{r}$

question 76

Multiple Choice

Find the value of the line integral $\int_{c} \mathbf{F} \cdot d \mathbf{r}$ on the closed path consisting of line segments from $( 0,2 )$ to $( 0,0 )$ , from $( 0,0 )$ to $( 2,0 )$ , and then from $( 2,0 )$ to $( 0,2 )$ , where $\mathbf { F } ( x , y ) = 3 y e ^ { 3 x y } \mathbf { i } + 3 x e ^ { 3 x y } \mathbf { j }$ .
(Hint: If $\mathbf { F }$ is conservative, the integration may be easier on an alternate path.)

• A) 99
• B) 12
• C) 36
• D) 30
• E) 0

---

Definitions:

Campfire

An outdoor fire created in a pit or ring of stones, typically used for warmth, cooking, or entertainment purposes.

Two-factor

A concept in psychology that suggests a phenomenon or outcome is the result of two distinct factors, often used in the context of emotion or motivation.

Theory of Emotion

A framework that attempts to explain how emotions are experienced, how they are elicited, and how they influence behavior and thought.

Presentation

The act of showing or displaying information or data, often in a public or formal setting.