(Solved):   Define two vector functions \[ \begin{array}{l} \vec{r}(t)=9 \sin (t) \vec{i}+5 \cos (t) ...

 

Define two vector functions \[ \begin{array}{l} \vec{r}(t)=9 \sin (t) \vec{i}+5 \cos (t) \vec{j}+11 t^{2} \vec{k} \\ \vec{u}(t)=5 \sin (t) \vec{i}+9 \cos (t) \vec{j}+(t-11) \vec{k} \end{array} \] Compute \( \vec{r}(t) \cdot \vec{u}(t)= \) Let \( \vec{r}(t)=\left\langle 4 t^{4}+2,-4 e^{-t}, 3 \sin (-t)\right\rangle \). Find \( \int \vec{r}(t) d t \) (don't include the \( +\mathrm{C} \) ) \[ \int \vec{r}(t) d t=\langle \]