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Math Help - [SOLVED] Integrability

  1. #1
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    [SOLVED] Integrability

    Is f(x,y) = (\sin(x) \sin(y)) / ({x^2 + y^2}) integrable over (-\pi/2,\pi/2) \times (-\pi/2,\pi/2)?
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  2. #2
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    Quote Originally Posted by Amanda1990 View Post
    Is f(x,y) = (\sin(x) \sin(y)) / ({x^2 + y^2}) integrable over (-\pi/2,\pi/2) \times (-\pi/2,\pi/2)?
    Here's my answer: since |\sin x\sin y|\leq |x||y|\leq \frac{1}{2}(x^2+y^2), we have |f(x,y)|\leq \frac{1}{2}. Thus f is bounded and continuous, except perhaps at the point 0 (doesn't matter), so that it is integrable on any bounded subset of \mathbb{R}^2.
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