Integration Thoughts

There are some tricky assumptions about integration that need to be addressed:

We know this from optimization theory - we need to be careful about integrating a function using usual methods - it could be the case in higher dimensions that a function is not integrable.

To prove that it is indeed Riemann integrable, we need to show that the measure of the boundary of the region has volume zero . This is also equivalent to showing:

  • the region is a Jordan region (what’s that?), or that
  • the set to integrate over is admissible, or that
  • the boundary of the volume to integrate is zero

Also… happy pi day!!!