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Evaluate the following line integral:

$$\int_C ze^{xy}ds$$

...where:

$$C: \vec{r}(t)=\langle t, -2t, t\rangle, t\in[0,2]$$

A

$\cfrac{\sqrt{6}}{4}(1-e^{-8})$

B

$\cfrac{\sqrt{6}}{2}(1+e^{-8})$

C

$\cfrac{\sqrt{6}}{4}(1-e^{-4})$

D

$\cfrac{\sqrt{6}}{2}(1-e^{-4})$

E

$0$

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