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## Homework Statement

Let [itex]\vec{F}: ℝ^{2}->ℝ^{2}[/itex] be a continuous vector field in which, for every [itex](x, y), \vec{F}(x, y)[/itex] is parallel to [itex]x\vec{i}+y\vec{j}[/itex]. Evaluate [itex]\int_{γ}\vec{F}\cdot d\vec{r}[/itex] where [itex]γ:[a, b]->ℝ^{2}[/itex] is a curve of class [itex]C^{1}[/itex], and it's imagem is contained in the circunference centered in the origin and with radius [itex]r>0[/itex].

## The Attempt at a Solution

We know that [itex]\vec{F}(x, y)=a(x\vec{i}+y\vec{j})[/itex], where [itex]a[/itex] is a constant, and we need to evaluate [itex]\int^{b}_{a}\vec{F}(γ(t))\cdot γ'(t)dt[/itex]. So?...

Thanks

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