Question: How to compute the arc length parametrization for a space curve (vector-valued function)

New question: 10/14/19

I have an arc length parametrization problem. I got the right answer for the speed. The lines of code before the long dividing line I successfully got to work. The main problem I am having is with the code underneath that. It is producing weird answers and just returning the same words without computing any mathematical calculation.

 

with(VectorCalculus):

with(plots):

T:= 4:

r := t -> <t^2 + t, sin(t^2)*(t + 1), cos(t^2)*(t + 1)>;

speed := Norm(diff(r(t), t));

evalf(Int(speed, t = 0 .. T)); (I got 62.98633182 for this part)

----------------------------This is where I started running into problems with the arc length parametrization.

L := b -> int(speed, t = 0 .. b);

speed := t -> subs(c = t, Norm(diff(r(c), c)));

speed2 := t -> sqrt(factor(simplify(speed(t)^2)));

solve(s = L(t), s);

assume(b > 0 'real');

g := s -> solve(s = L(b), b, useassumptions = true);

newr := s -> r(g(s));

newr(s);

 

 

 

(old question from 10/6/19)

I have an arc length parametrization question. The problem says to find a function g(s) that you can use to calculate the arc length parametrization, then find a formula for the arc length parametrization. I have r(t)= <cos(2t), sin(3t), 4t>. How would I do this?

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