Calculate (mathbf{F}=abla f), where (f(x, y, z)=x y e^{z}), and compute (int_{C} mathbf{F} cdot d mathbf{r}), where:

Question:

Calculate $\mathbf{F}=abla f$, where $f(x, y, z)=x y e^{z}$, and compute $\int_{C} \mathbf{F} \cdot d \mathbf{r}$, where:
(a) $C$ is any curve from $(1,1,0)$ to $(3, e,-1)$.
(b) $C$ is the boundary of the square $0 \leq x \leq 1,0 \leq y \leq 1$ oriented counterclockwise.

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