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Math Help - fubini's theorem

  1. #1
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    fubini's theorem

    show the function f(x,y)=\frac{x^2-y^2}{(x^2+y^2)^2} is not Lebesgue integrable on (0,1)X(0,1).

    Apply Fubini's theorem and use \frac{x^2-y^2}{(x^2+y^2)^2}=\frac{1}{x^2+y^2} + \frac{y(-2y)}{(x^2+y^2)^2} and \frac{d}{dy}\frac{1}{x^2+y^2}=\frac{-2y}{(x^2+y^2)^2}

    i have been stuck on this for a while. help me please.
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  2. #2
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    fubini theorem

    when i computed the integral \int \int \frac{x^2-y^2}{(x^2+y^2)^2} dy dx, i got - \infty. does it mean it is not lebesgue integrable. i do not know in general what i have to show to say it is not lebesgue integral. im grateful for any help please.
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  3. #3
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    See here:

    Fubini's theorem - Wikipedia, the free encyclopedia

    They address this exact problem when explaining Fubini's theorem.
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