Question: Compute the line integral (int_{mathbf{c}} mathbf{F} cdot d mathbf{r}) for the given vector field and path. (mathbf{F}(x, y)=leftlangle x^{2} y, y^{2} z, z^{2} xightangle), the

Compute the line integral $\int_{\mathbf{c}} \mathbf{F} \cdot d \mathbf{r}$ for the given vector field and path.

$\mathbf{F}(x, y)=\left\langle x^{2} y, y^{2} z, z^{2} xightangle$, the path $\mathbf{r}(t)=\left\langle e^{-t}, e^{-2 t}, e^{-3 t}ightangle$ for $0 \leq t<\infty$

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