Improper Integrals

Saturday, 9 June 2018

6:10 PM

Consider  as

 is said to be integrable over  and the integral is said to be convergent

 

Consider  does not have a limit

 is said to be not integrable over  and the integral is said to be divergent

 

 is said to be integral over  if it is also integrable over  and .

Otherwise, it is considered to diverge

 

 

Convergence and divergence of p-integrals

If , then the integral is convergent

If , then the integral is divergent

 

Comparison tests to determine the behaviour of harder integrals

Compare with a more common integral