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Find the arc length \( s \) of the vector function \( \mathbf{r}(t)=3 \cos ^{3}(t) \mathbf{i}+3 \s ...
Find the arc length \( s \) of the vector function \( \mathbf{r}(t)=3 \cos ^{3}(t) \mathbf{i}+3 \sin ^{3}(t) \mathbf{j}+\mathbf{k} \) from \( t=0 \) to \( t=\frac{\pi}{2} \). (Give an exact answer. Use symbolic notation and fractions where needed.) \[ s= \]