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Proper mathematical notation in regarding integrals

  1. Jul 11, 2012 #1
    Hi

    I have a question regarding notation. I have a function f(x, y), which I would like to integrate as
    [tex]
    \int_{x>0,y<x\frac{1}{\sqrt{\pi}}+1}{f(x, y) dxdy}
    [/tex]
    My question is very simple, and probably very silly: What there a notation which enables me to write the condition for the integral (x>0, y ....) in a much shorter version? I thought about defining a set myself called α, which is defined by this condition and then just write
    [tex]
    \int_{\alpha}{f(x, y) dxdy}
    [/tex]
    But I am not sure if I am allowed to do this. Even if I am allowed to do this, I don't know how to properly define the set. I would be very happy to recieve some professional help.

    Best wishes,
    Niles.
     
  2. jcsd
  3. Jul 11, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Niles! :smile:

    You can either write it with two ∫ signs …
    [tex]
    \int_{x>0}\int_{y<x\frac{1}{\sqrt{\pi}}+1}f(x, y) dxdy
    [/tex]

    or you can write it
    [tex]
    \int_A f(x, y) dxdy
    [/tex]

    and state separately that A is the region [itex]x>0,y<x\frac{1}{\sqrt{\pi}}+1[/itex]
     
  4. Jul 11, 2012 #3
    Hi

    Thanks for that.

    Best,
    Niles.
     
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