Let (I=oint_{C} mathbf{F} cdot d mathbf{r}), where (mathbf{F}(x, y)=leftlangle y+sin x^{2}, x^{2}+e^{y^{2}}ightangle) and (C) is the circle

Question:

Let $I=\oint_{C} \mathbf{F} \cdot d \mathbf{r}$, where $\mathbf{F}(x, y)=\left\langle y+\sin x^{2}, x^{2}+e^{y^{2}}ightangle$ and $C$ is the circle of radius 4 centered at the origin.
(a) Which is easier, evaluating $I$ directly or using Green's Theorem?
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