Exploring Integration by Foliation: Resources for Advanced Calculus Concepts

[bolbteppa]

I posted a question on stack about generalizing the methods of volumes by slicing & volumes of revolutions & came across the notion of integration by foliation. I'm wondering if there are any resources you guys know of where I could delve into this further, I'd love to think in a sophisticated & unified manner about ideas like surface area of revolution, volumes by cross-sectional areas, volumes of revolution, etc... but don't know what to do or where to go, & I'm sure there's something out there on these topics, thanks

 

[ZetaGuy]

You may take a look at Volumes of Solids of Revolution. A Unified Approach which cites the article by Walter Carlip, Disks and Shells Revisited and Eric Key, Disk Shells and inverse functions, both collected in A calculus collection

There is an area of differential geometry that has the concept of foliations, but these are not exactly the same type of foliations mentioned in the stackexchange answer.

 

[bolbteppa]

Thanks a lot for the links, although they don't target the foliation aspect of my question they are great in and of themselves.