(Solved): 1 point) Let \( \vec{F}=14 x e^{y} \vec{i}+7 x^{2} e^{y} \vec{j} \) and \( \vec{G}=14(x-y) \vec{i}+ ...

1 point) Let \( \vec{F}=14 x e^{y} \vec{i}+7 x^{2} e^{y} \vec{j} \) and \( \vec{G}=14(x-y) \vec{i}+7(x+y) \vec{j} \). Let \( C \) be the path consisting of lines from \( (0,0) \) to \( (6,0) \) to \( 6,2) \) to \( (0,0) \). Find each of the following integrals exactly: (a) \( \int_{C} \vec{F} \cdot d \vec{r}= \) (b) \( \int_{C} \vec{G} \cdot d \vec{r}= \)