Arc Length Calculus III

Question

For the curve defined by

→r(t)=5cos(t)→i+5sin(t)→j+2t→k

evaluate

s=∫(upper limit =t and lower limit =0) ||→r'(u)||du

I found the arc length function which was rad 29 t

I also found the arc length function for t which was s/ rad 29

The last question is the following:

Parametrize →r(t)r→(t) by arc length by substituting in the solved arc length function.

How would I do this last step?

Answer 1

I believe that all you have to do is to substitute s/sqrt(29) for t in the expression for r(t). This will give r(s)