1. ## 2 dimensional integral

Can some one give me an example of a 2 dimensional integral over a region Q, such that one of the iterated integrals exist, but the other does not.

I have tried sort of taking examples of functions that are not continuous, but the ones I have set up, just don't fit into the description.
I appreciate any help I can get.

2. ## Re: 2 dimensional integral

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 [LaTeX ERROR: Compile failed] . The first integral, from 0 to 1/x, with respect to y, exists and is 1/x. The second integral, then, is [LaTeX ERROR: Compile failed] which does not exist.

Or do you mean [LaTeX ERROR: Compile failed] , say, exists, but [LaTeX ERROR: Compile failed] does not? In that case, if one exists, the other must and must give the same result.

3. ## Re: 2 dimensional integral

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.
repost to fix latex