# Thread: Find length of the curve help

1. ## Find length of the curve help

find the length of the curve r(t) = <2t, t^2, 1/3t^3>

I did this
r'(t) = <2, 2t, t^2>

|r'(t)|

When I take the integral, I don't know how to solve for it.

2. Originally Posted by khuezy
find the length of the curve r(t) = <2t, t^2, 1/3t^3>

I did this
r'(t) = <2, 2t, t^2>

|r'(t)|

When I take the integral, I don't know how to solve for it.
Second, the integral is $\int_{t_0}^{t_f}\sqrt{\left(\frac{\,dx}{\,dt}\righ t)^2+\left(\frac{\,dy}{\,dt}\right)^2+\left(\frac{ \,dz}{\,dt}\right)^2}\,dt=\int_{t_0}^{t_f}\sqrt{4+ 4t^2+t^4}\,dt=\int_{t_0}^{t_f}\sqrt{(t^2+2)^2}\,dt$ $=\int_{t_0}^{t_f}\left(t^2+2\right)\,dt$, for $t_0\leq t\leq t_f$