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

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) $0$

Correct Answer:

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