- Reminder: Calc lab (ST 243) hours:
Mondays: 8:30am- 1:45pm Tuesdays: 10:45am- 1:30pm Wednesdays: 8:30am-12:30pm Thursdays: 10:45am- 4:00pm Fridays: 8:30am-12:00pm
Give it a try. Show up with your homework, and when you get stuck -- ask!
- You should get your calculator set up so that you can do these numerical methods quickly.
- One more from section 8.1:
- #41, p. 422
- Anything else on your minds?
- In this section we deal with integrals of two sorts: those whose limits of integration are infinite, and those with vertical asymptotes.
- Definition concerning the first type:
Here's an important example:
Let's just take a moment to check that it works, using a handout.
- The following figure illustrates the first type, and also the
second:
The integral exists over
But what can we say about the integral over
:
- There's a general rule for powers (it's easy to take the limits
and check):
Let's check in this case:
The case of p=1 is interesting, and we can use symmetry to see that it is so.
- There's a third component of this section which is interesting:
the idea of using bounding to deduce whether an integral
diverges or converges. For example, we can use comparison to
show that, in fact,
This one has infinite limits on both ends -- how do we handle that?
- We could use symmetry, of course; but more generally,
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?
- We could use symmetry, of course; but more generally,
- Examples:
- #13, p. 464
- #12, p. 464
- #43, p. 465
- #60, p. 465