Answer
$$s = 3\sqrt {10} $$
Work Step by Step
$$\eqalign{
& {\bf{r}}\left( t \right) = 3t{\bf{i}} - t{\bf{j}},{\text{ }}\left[ {0,3} \right] \cr
& {\text{Differentiate }}{\bf{r}}\left( t \right) \cr
& {\bf{r}}'\left( t \right) = \frac{d}{{dt}}\left[ {3t{\bf{i}} - t{\bf{j}}} \right] \cr
& {\bf{r}}'\left( t \right) = 3{\bf{i}} - {\bf{j}} \cr
& {\text{Find }}\left\| {{\bf{r}}'\left( t \right)} \right\| \cr
& \left\| {{\bf{r}}'\left( t \right)} \right\| = \sqrt {{{\left( 3 \right)}^2} + {{\left( { - 1} \right)}^2}} \cr
& \left\| {{\bf{r}}'\left( t \right)} \right\| = \sqrt {10} \cr
& {\text{Find the arc length }}s{\text{ using the formula }}s = \int_a^b {\left\| {{\bf{r}}'\left( t \right)} \right\|} dt \cr
& s = \int_0^3 {\sqrt {10} } dt \cr
& {\text{Integrate}} \cr
& s = \left[ {\sqrt {10} t} \right]_0^3 \cr
& s = 3\sqrt {10} \cr
& \cr
& {\text{Graph}} \cr} $$
