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

Evaluate $\int _ { c } \mathbf { F } d \mathbf { r }$ where $\mathbf { F } ( x , y ) = \left( \frac { - y } { x ^ { 2 } + y ^ { 2 } } , \frac { x } { x ^ { 2 } + y ^ { 2 } } \right)$ is the curve $C$ is given by $C : x = 5 \cos t , y = 5 \sin t , 0 \leq t \leq 2 \pi$ .

A) $10 \pi$
B) $- 2 \pi$
C) $- 4 \pi$
D) $\pi$
E) $- 10 \pi$
F) $2 \pi$
G) $4 \pi$
H) $0$

Correct Answer:

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