Evaluate the Line Integral $\int _ { C } y d x - x d y$

question 34

Multiple Choice

Evaluate the line integral $\int _ { C } y d x - x d y$ along the circle $x = 2 \cos t , y = 3 \sin t , 0 \leq t \leq 2 \pi$ .

• A) \(0\)
• B) \(- 24 \pi\)
• C)\(- 6 \pi\)
• D) \(- 12 \pi\)
• E)\(- \frac { \pi } { 2 }\)
• F)\(24 \pi\)
• G)\(6 \pi\)
• H) \(12 \pi\)

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Definitions:

Meaningful Patterns

Sequences or arrangements that hold significance or convey a particular message, often discerned through analysis or intuition.

Drawing

The act or skill of making images or diagrams by making lines and marks, especially with a pen or pencil, on paper.

Recognizable Objects

Items or shapes that can easily be identified or named due to their familiar characteristics.

Odd Shapes

Odd shapes refer to geometrical figures that do not conform to standard or recognized forms, often used in discussions of abstract or unusual visual patterns.