Improper Integrals

Here is a link to our Prezi. Although it explains most everything you need to know about improper integrals, we'll still explain it in this well versed blogosphere post.

An improper integral is an integral with limits that go out to infinity, OR it's an integral with an infinite discontinuity between its parameters.

They can look like this:









Or like this:


We began by using the example:





The graph of this is:



We're trying to find out whether the AUC of this graph is decreasing fast enough that it approaches a number. If the AUC of a graph approaches a finite number, then the limit is said to
CONVERGE
If the graph's integral approaches a number like infinity, then the integral is said to
DIVERGE

We need to find out if this graph is convergent or divergent, so to do that, we set up our limit like this:
 
Then you integrate with respect to t before plugging in the limits, like this:

Then you plug in infinity for t, which simplifies your answer to:
1
Since this limit approaches a finite number, this example is
CONVERGENT
#swag #calrobbins #limitswag #whatwhat? #OBisthebest #A+Blogpost

Patrick JMT also did his own version of this limit. If you like him better, or if you just don't like us, then watch him. Then look at this:
 
Side-splitting laughter. I know.

We also showed the class this wonderful video which shows an infinite discontinuity at an endpoint, and then we ended this class with wonderful questions from wonderful people and some other not so wonderful people.

Thanks for a great year guys! We'll miss you all.

Well...most all of you.




 #CalRobbins and #EddieMcCluskey OUT.