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

question 12

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 $C : x = 5 \sin t , y = 5 \cos t , 0 \leq t \leq 4 \pi$ .

• 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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