I know certain things about small finite increments, like how the general formula for dy/dx is derived, but I have no idea how to manipulate the infinitesimals. The assumptions made seems arbitrary to me, how do I know that it is ok to assume one thing, but wrong to assume in case of others? I mean I can understand that this follows from that assumption and etc, but what made the assumptions valid I have no idea. Can you please explain to me the concept of delta x, or give me links to some resources so that I can understand at least well enough to get sums like these done from scratch:
If you are talking about problem 19, a hemi-spherical shell, each band has bases of two different sizes- part of a cone, not a cylinder.And if using the formula for cylinder's volume is ok, why is it not ok to use cylinder's height (which I calculated) instead of slant height?