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.
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));