# Integral Convergance

• Jun 29th 2010, 01:42 AM
GIPC
Integral Convergance
Does the following integrals converge, and what test should I apply?

http://img812.imageshack.us/img812/9831/capturehj.jpg
• Jun 29th 2010, 01:58 AM
CaptainBlack
Quote:

Originally Posted by GIPC
Does the following integrals converge, and what test should I apply?

http://img812.imageshack.us/img812/9831/capturehj.jpg

For the first change the variable to $u=1/x$ then it should be relativly easy, and what method you use depends on what you have been taught, I would look at the asymtotic behaviiour at zero and infinity.

CB
• Jun 29th 2010, 06:45 AM
GIPC
I still don't see how that helps.(Worried)
• Jun 29th 2010, 07:41 PM
CaptainBlack
Quote:

Originally Posted by GIPC
I still don't see how that helps.(Worried)

For one thing it gets rid of the infinite number of oscillations of the integrand at the lower limit of integration, leaving you with a more conventional problem.