Multivariate Calculus: integral w.r.t. arclength, reversals and reparametrization 9-7-23 part 2

[jamescook]

I should correct the divergence comment, I should have been graphing sideways, it's the value of 2t^2 which goes into the tangent and causes the problem. The question is where can 2t^2 attain integer and a half multiples of pi as t goes from 0 to 4. The answer is a bunch, but for instance 2t^2 = pi/2 gives t = sqrt(pi/4) as the first troublesome t-value which I would need to approach as an improper integral...