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An integral inequality: Source?

  1. Mar 20, 2005 #1
    I know this is probably a gross generalization of what the actual inequality states, but I'm wondering if someone can tell me the origin of this integral inequality (or something resembling it :/ ):

    [tex]|\int f(x)| \leq \int|f(x)|[/tex]

    This is my first time using latex, so I hoped that turned out ok. Any suggestions on that too would be appreciated! Thanks.
     
    Last edited: Mar 20, 2005
  2. jcsd
  3. Mar 20, 2005 #2
    I don't understand your question...

    the left side just takes the absolute value of the area under f(x), which could well be negative. As for the right side, it will count a negative f(x) as positive... if it's applied to a velocity function, it would give the total distance travelled rather than displacement for example.
     
  4. Mar 20, 2005 #3
    [tex]|\int f(x)| \leq \int|f(x)|[/tex]

    This is not a terribly interesting equality, I am sure that you could form a proof. I can only guess that you are trying to discuss the cauchy-schwarz inequality:

    http://mathworld.wolfram.com/SchwarzsInequality.html

    Which is reasonably famous but very uninteresting.
     
  5. Mar 20, 2005 #4
    It's just an application of the triangle inequality.
     
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