Hey sorry for another thread but I just did this question and am not very sure about my answer...



So I get this as the arc length function



Not very pretty... anyway on part b it asks me to reparametrize by arc length so I solve for t in terms of s. As you can tell it ends up even uglier. There's not much simplifying either (only in the radius), the things inside cost and sint are really bad. I was just wondering if I should expect for things to simplify nicely with this reparametrization, or is there something I am missing or doing wrong?

Any insight would be appreciated, thanks!

i dont think it will simplify any further.

rearranging gives

t = -ln[-bs/(a*sqrt(b^2+1)) + 1 ]/b which as u said is really ugly to work with.

but when u calculate curvature, i would recommend making a sub for -b/(a*sqrt(b^2+1)) = c since they r constants

Okay just making sure, thanks