Find the arc length parametrization of a curve

[AramN]

Homework Statement

Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) .

Homework Equations

s(t)=integral of |r'(t)| dt

The Attempt at a Solution

I was able to get the integral of the magnitude of the velocity vector to simplify to:
s(t) = integral of sqrt(9(1+t)^2) dt
evaluating the integral, s(t) = 3t+(3/2)t^2
In other problems similar to this one I would solve for t in terms of s then put it back into the original equation, but for this one I was unable to solve for t in terms of s.

 

[Dick]

Homework Statement

Find the arc length parametrization of the curve r = (3t cost, 3tsint, 2sqrt(2)t^(3/2) ) .

Homework Equations

s(t)=integral of |r'(t)| dt

The Attempt at a Solution

I was able to get the integral of the magnitude of the velocity vector to simplify to:
s(t) = integral of sqrt(9(1+t)^2) dt
evaluating the integral, s(t) = 3t+(3/2)t^2
In other problems similar to this one I would solve for t in terms of s then put it back into the original equation, but for this one I was unable to solve for t in terms of s.

I don't see the problem in solving for t. It's just a quadratic equation.