Hello,
I need to show that an integral from minus infinity to infinity is smaller than infinity. All the expressions that are integrated are positive. What should I do? Can you recommend me some theorems that I can use? Thank you in advance!
Hello,
I need to show that an integral from minus infinity to infinity is smaller than infinity. All the expressions that are integrated are positive. What should I do? Can you recommend me some theorems that I can use? Thank you in advance!
As |x| and x^2 are positive, we can write this as,
So checking the convergence of is enough.
We can easily prove that converges.
For ,
So converges too.
Now prove the convergence of and it'll be over.
(It looks a little long and I can't think of anything easy at the moment..)