Page 47 - Calculus for the Clueless, Calc II

Each bracketed piece goes to infinity. The integral diverges. However, if you did the problem, you should
calculate only one piece. Once it diverges, you need not do the other piece.

The next two are a couple of my most favorite examples. It makes you believe that mathematicians can do
anything. This is not true, of course, but the examples are extraordinary.

Example 7—

We will take an infinite area, rotate the region, and get a finite volume!!!!!!!!! Here's our infinite area:

Volumes are determined by sections. Much more on this is in Chap. 11 in this book.

Amazing!!!!!! Infinite area rotated gives finite volume.

This one will totally blow your mind. We will now take a finite region, rotate it, and get an infinite volume,
which would seem impossible after the last example. It is not!!!!

Example 8—