with $a,b \in \mathbb{R}$ and $-1 <a<b<1$.
I tried to compute the 2 dimensional volume of the set M (the area) by submanifolds. But I have hard times finding an right atlas for it. I tried it with $\phi(x,z)=(x,\sqrt{1-x^2-z^2},z)$ but it seems like that it doesn't work with this one and now I am stuck. So how can I find an easy way to compute this by submanifolds? What am I missing?
As hint we got $\int \frac{dx}{\sqrt{a^2-x^2}}=\sin^{-1}(\frac{x}{a}) +C$. Maybe for the late part of the solution.
The question was asked before here but, I guess the questioner didn't provide the right and enough information for the problem. )