I want to integrate $$\int_0^a \sqrt{1+\left(\frac{d\delta(x)}{dx}\right)^2} dx$$
Where $$ \delta(x) = C_1 \sqrt{a^2-x^2} \left(C_2 \left(\frac{x}{a}\right)^3+C_3 \left(\frac{x}{a}\right)^2+C_4(\frac{x}{a})+C_5\right)$$
I think I may be able to do this with some form of coordinate transform, but I just don't see it at this moment. I also banged it into Wolfram Mathematica with no success. Any help would be appreciated.