Calculate the work done by the field \(\mathbf{F}\) when the object moves along the given path from the initial point to the final point.

\(\mathbf{F}(x, y, z)=\left\langle e^{x}, e^{y}, x y zightangle, \mathbf{r}=\left\langle t^{2}, t, t / 2ightangle\) for \(0 \leq t \leq 1\)