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Integration via Foliation

  1. Sep 5, 2013 #1
    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 :approve:
  2. jcsd
  3. Sep 8, 2013 #2
    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.
  4. Sep 9, 2013 #3
    Thanks a lot for the links, although they don't target the foliation aspect of my question they are great in and of themselves.
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