Hey so I have looked through other threads, and searched online but I can't find a good explanation as to why the surface area of revolution is 2π$\int y\sqrt{1+\frac{dy}{dx}^2}\ dx$ and not just 2π$\int y dx$
Since for volume of revolution its π$\int y^2 dx$, as its just integrating each area to get the volume with $\pi r^2$, so why can't you just integrate each perimeter to get the surface area to get 2π$\int y dx$?
For context this is the surface area I am trying to find where $y=x^3$.
