I'm kind of confused about the explanation of the surface area formula in my text book
The text gave us $$\int_{a}^{b}2\pi f(x) \sqrt{1+[f'(x)]^2}dx$$ after that the formula is getting like $$\int_{a}^{b}2\pi y \sqrt{1+\left(\frac{dy}{dx}\right)^2 }dx$$
also it said $$\int_{a}^{b}2\pi y \sqrt{1+ \left(\frac{dx}{dy}\right)^2 }dy$$
They used $y$ instead of $f(x)$. It confused me.
How can I figure out between when I plug in some $y$ function at $y$ and when I change any thing (just use $y$) in the formula?
Kind of difficult to explain though, I hope you can understand my question. And if you have any idea, please post it. Thank you!