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

question 79

Multiple Choice

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

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

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