Originally Posted by

**HallsofIvy** Here's a simple example: Find the area between the graph of y= 1/x and y= 0, from x= 1 to infinity.

That would be $\int_1^\infty \int_0^{1/x} dydx$. The first integral, from 0 to 1/x, with respect to y, exists and is 1/x. The second integral, then, is $\int_1^\infty \frac{1}{x} dx= \left[ln(x)\right]_1^\infty$ which does not exist.

Or do you mean $\int\int f(x,y)dxdy$, say, exists, but $\int\int f(x,y)dydx$ does not? In that case, if one exists, the other must and must give the same result.