Question

I am having some understanding issues. Why is it that when we calculate volume we integrate over dx/dy and when calculating surface area we integrate over ds? I am referring of course to surface of rotation.

Answer 1

anyone please???? For example when they calculated the volume of the sphere they used disks, and when calculating area of sphere it was integrating with respect to ds

Answer 2

I also have the same doubt, but I could not find a satisfactory answer yet. The best I understood is that for volume, the error in approximating the curve to dx is acceptable, but for surface area not, so you need to use ds.

Answer 3

yeah, i kind of reached the same conclusion, it kind of sucks