Last time: Started 8.6 | Next time: Start 9.4 |
Today:
Here's an important example:
The integral exists over But what can we say about the integral over :
Last time we checked in this case:
As noted last time, the case of p=1 is interesting, and we can use symmetry to see that the area is unbounded in both cases.
Last time we checked that these work using a handout. Let's do a few more, to get warmed up for today's new material: convergence.
Examples:
This one has infinite limits on both ends -- how do we handle that?
How would we use comparison? We find a function which is everywhere greater than the function but which has finite area. Can you think of a good candidate?
Let's use my choice and this handout. What are the issues?