Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$

question 10

Multiple Choice

Evaluate $\int _ { C } \mathbf { F } d \mathbf { r }$ where $\mathrm { F } ( x , y ) = \left( \arctan y , - \frac { x y ^ { 2 } } { 1 + y ^ { 2 } } \right)$ and the curve C is given by C : $x = 2 \cos t , y = 2 \sin t , 0 \leq t \leq 2 \pi$ .

• A) \(2 \pi\)
• B) \(12 \pi\)
• C)\(4 \pi\)
• D) \(\pi\)
• E)\(- 2 \pi\)
• F) \(- 12 \pi\)
• G) \(- 4 \pi\)
• H) \(0\)

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