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General Integral Question

  1. Oct 15, 2011 #1
    Is there any function such that:
    [itex]_{-∞}[/itex][itex]\int[/itex][itex]^{∞}[/itex]f(x) dx
    Is any integer except 0 and ∞?
  2. jcsd
  3. Oct 15, 2011 #2
    f(x) can be impulse function
  4. Oct 15, 2011 #3
    I'm not sure what omkar meant by impulse function but if f(x)=[itex]\frac{1}{1+x^2}[/itex], the integral will not equal 0 or ∞.
  5. Oct 15, 2011 #4
    I looked it up, apparently is an equation that satisfies the statement that the integral from -∞ to ∞ is 1, but because of the way it's defined it isn't actually a function.
  6. Oct 16, 2011 #5


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    There are an infinite number of such functions. For example:
    [tex]\int^\infty_{-\infty}e^{-x^2}dx = \sqrt{\pi}[/tex]
    so if:
    [tex]f(x) = \frac{7}{\sqrt\pi}e^{-x^2}[/tex]
    [tex]\int^\infty_{-\infty}f(x)dx = 7[/tex]
    There are lots of functions like this that one can play this game with.
  7. Oct 16, 2011 #6
    Ohhhh. That is very interesting. This is the first time I have ever heard of that.

    Cool! That looks fun lol.
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