Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Total vs partial integration

  1. Oct 31, 2012 #1
    Hi,

    Is there a difference between

    [tex] \int f(x,y(x)) dx [/tex]

    And

    [tex] \int f(x,y(x)) \partial x [/tex]

    ???

    If so, how is the total integral written in terms of partial integrals?

    Thanks for your help.
     
  2. jcsd
  3. Oct 31, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I have never seen [itex]\partial[/itex] used in that way.
     
  4. Oct 31, 2012 #3
    In both cases, the function f is dependent on x only.

    If by partial integration, you mean an iterated integral, then the result of both should be the same.

    Either way, the iterated integral uses a total differential dx, not a partial.
     
  5. Oct 31, 2012 #4

    lurflurf

    User Avatar
    Homework Helper

    The dx usually means partial integration. The ∂x is an added reminder of partial integration it is sometimes used when solving exact differential equation as a reminder. Writing y(x) is also a clear indicator of functional dependence, more clear than writing y.
     
  6. Oct 31, 2012 #5

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Neither have I, and as other posts here point out x is the only independent variable in the OP, so it cannot make any difference.
    More generally (when there's another independent variable), it could make sense as a path integral, i.e. along a path where the other independent variable is constant.
     
  7. Oct 31, 2012 #6

    lurflurf

    User Avatar
    Homework Helper

    Have none of you read the CRC Handbook of Chemistry and Physics?
     
  8. Nov 1, 2012 #7

    Mute

    User Avatar
    Homework Helper

    I've never seen ##\partial## used that way either (I haven't throughly read the CRC handbook, it seems), but if I had to wager a guess I would suppose that

    $$\int f(x,y(x))\partial x$$
    is meant to be integrated in only the first argument, holding y=y(x) fixed, while

    $$\int f(x,y(x)) dx$$
    is meant to be integrated over all of the x-dependence.

    But, without some more context, I could be entirely wrong here.
     
  9. Nov 1, 2012 #8
    Thanks for your help everyone. My question has been answered above and beyond.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Total vs partial integration
  1. Partial integration (Replies: 1)

Loading...