I know how to find arc length and set up the equation in normal circumstances, but I have failed in all attempts to even set up this problem. I cannot even find a good example similar to this to get me on the right track. How would I go about solving it?
Thank you for the help!
Hint: In order to compute the arc length, you set up an integral of the form $\int ds=\int \sqrt{dx^2+dy^2}.$ The 'usual' route is to say that $y=f(x)$, then find $dy/dx$ and use this to obtain an integral with respect to $x$. That's not practical here, but do you see a convenient alternative?
One thing that may clarify the problem's intention: you're given $x$ as a function of $y$ in the form of a definite integral. So you do have a curve, just not given explicitly.