Question

I need help understand the concept/"pattern" involving Improper Integrals!

Answer 1

if there is an offending zero in the integral, cut it out and take the limit as it approaches it

Answer 2

or if you have to integrate to inf ... take the limit of the integral as it approaches inf

Answer 3

@SirSantaofClaus, You may be able to find what you are looking for here:

http://tutorial.math.lamar.edu/Classes/CalcII/ImproperIntegrals.aspx

Answer 4

Thanks, I have been on Paul's Notes for a few weeks now - great resource, but I often need multiple interpretations before I finally comprehend a new section in math (especially the confusing limits)
This site has helped clarify things for me... http://math.ucsd.edu/~wgarner/math20b/improper_integrals.htm

Answer 5

That site only introduced the application of improper integrals for determining whether they converge or diverge. And the process of determining that works great for continuous functions. Paul's online notes further addresses the set of cases for discontinuous functions.

Answer 6

I can do indefinite/definite integrals all day long, but for some reason when I came to this section, I'm having a difficult time understanding/"seeing" what is happening. The gist of what I have absorbed so far is that improper integrals is some type of indefinite integral that you pick a variable to convert it into a definite integral.... is this the correct way of thinking?

Answer 7

That's pretty much the gist of it, since you already know how deal with definite integrals. It is basically applying what you already know to the new concept of improper integrals. Unfortunately, along with this new concept comes another set of rules you must master.

Answer 8

Just to clarify, when talking about definite integrals, we mean, \[\int\limits_{a}^{b}f(x)dx = F(b)-F(a)\] right?

Answer 9

Of course bro.

Answer 10

Thanks, it was a dumb question - but I'm super stressed, so I just need to make sure there wasn't something I forgot :D

Answer 11

No such thing as a dumb question where you're studying calc bro.