That is the entire original question. It didn't come out of a textbook, if that's what you're asking. Here's a graph of superimposed on :
http://i51.tinypic.com/avk3v7.jpg
Gold is the former, green the latter. Essentially what I'm trying to do is find an inverse function for .
Maxima (my computer algebra system) is unable to solve the original equation for b in terms of x.
EDIT: sorry... I sorta implied it in my original post, but I guess I should be more explicit. is the arc length of the function from 0 to some x.