Question

Evaluate s(t)=∫t−∞||r′(u)||dus(t)=∫−∞t||r′(u)||du for the Bernoulli spiral r(t)=〈etcos(4t),etsin(4t)〉r(t)=〈etcos⁡(4t),etsin⁡(4t)〉.
It is convenient to take −∞−∞ as the lower limit since s(−∞)=0s(−∞)=0. Then use ss to obtain an arc length parametrization of r(t)r(t).

r1(s)=〈r1(s)=〈  , 〉

Answer 1