[SOLVED] Integrability

Quote:

Originally Posted by Amanda1990

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 $\mathbb{R}^2$ .