timray60,
I did not see your solution to this exercise before I commenced my own. (I sorted the posts by subject, and because the "paper clip" sorts at the bottom I missed it)
Thanks for your explanation why

is equivalent to

.
I have a problem with your substitution of

limits of

to

. I see how it is correct, because you have this ray or half line from the

to

that you are integrating over

to cover the whole plane. However, I don't see how you are getting there from your math. Could you look at my solution and tell me if you think I am wrong the way I do it?