Can you add or subtract infinity?
It is impossible for infinity subtracted from infinity to be equal to one and zero. Therefore, infinity subtracted from infinity is undefined.
How do you replace infinity in integration?
When both of the limits of integration are infinite, you split the integral in two and turn each part into a limit. Splitting up the integral at x = 0 is convenient because zero’s an easy number to deal with, but you can split it up anywhere you like.
What is the interval of integration over infinity?
In this kind of integral one or both of the limits of integration are infinity. In these cases, the interval of integration is said to be over an infinite interval. Let’s take a look at an example that will also show us how we are going to deal with these integrals. This is an innocent enough looking integral.
How do you deal with the infinite limits of integrals?
The process we are using to deal with the infinite limits requires only one infinite limit in the integral and so we’ll need to split the integral up into two separate integrals. We can split the integral up at any point, so let’s choose x = 0 x = 0 since this will be a convenient point for the evaluation process.
What are improper integrals?
In this section we need to take a look at a couple of different kinds of integrals. Both of these are examples of integrals that are called Improper Integrals. Let’s start with the first kind of improper integrals that we’re going to take a look at. In this kind of integral one or both of the limits of integration are infinity.
What is the difference between convergent and divergent integrals?
We will call these integrals convergent if the associated limit exists and is a finite number (i.e. it’s not plus or minus infinity) and divergent if the associated limit either doesn’t exist or is (plus or minus) infinity. Let’s now formalize up the method for dealing with infinite intervals.