Question: Compute the line integral (int_{mathbf{c}} mathbf{F} cdot d mathbf{r}) for the given vector field and path. (mathbf{F}(x, y)=leftlanglefrac{2 y}{x^{2}+4 y^{2}}, frac{x}{x^{2}+4 y^{2}}ightangle), the path (mathbf{r}(t)=leftlanglecos

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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