Find length of the curve help

**khuezy** · November 4th 2008, 08:31 PM

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.
Thanks in advanced.

**Chris L T521** · November 4th 2008, 09:15 PM

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.
Thanks in advanced.

First, what are the boundaries on t?

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 $t_0\leq t\leq t_f$

This is not much of a hassle to integrate.

Does this make sense?

--Chris

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