## Calculus (3rd Edition)

$$4\sqrt{13}.$$
We have $r(t) =2ti-3tk$, and so $r'(t) =2i-3k$. We calculate the length by integration: $$length=\int_{11}^{15}\sqrt{4+9}dt=\sqrt{13}t|_{11}^{15}=4\sqrt{13}.$$