Compute the line integral (int_{mathbf{c}} mathbf{F} cdot d mathbf{r}) for the given vector field and path. (mathbf{F}(x,
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Compute the line integral \(\int_{\mathbf{c}} \mathbf{F} \cdot d \mathbf{r}\) for the given vector field and path.
\(\mathbf{F}(x, y)=\left\langle\frac{2 y}{x^{2}+4 y^{2}}, \frac{x}{x^{2}+4 y^{2}}ightangle\), the path \(\mathbf{r}(t)=\left\langle\cos t, \frac{1}{2} \sin tightangle\) for \(0 \leq t \leq 2 \pi\)
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