From ChatGPT: "When you revolve a curve $y=f(x)$ around the x-axis, you are generating a surface composed of infinitesimally thin strips that are themselves small frustums (truncated cones).
Each of these strips' surface area depends on the true length of the curve over that small segment (to account for infinitely small changes in x and y).
Even though dx is infinitely small, the differential element ds accurately represents the true length of the curve segment by considering both the horizontal change ($dx$) and the vertical change ($dy$)."
But isn't the surface area of an infinitely thin frustum, the same as the surface area of an infinitely thin cylinder? I mean, the difference is negligible! If it's infinitely thin and there are infinitely many?
Why would I at all need the arc length component, just $dx$ is enough in the integral, right?
