Thread: Integral Divergence or Convergence Using Comparison Theorm

The question is;
Use the Comparison theorm to determine wheater the integral is convergent or divergent.

I) integral (cosx)^2*dx/1+x^2 a=1 b=infinte

II) integral dx/x+ e^2x a=1 b=infinte

Answers are I=Convergent, II=convergent

Help Much Appreciated!

Here are some hints

Originally Posted by zangestu888

Use the Comparison theorm to determine wheater the integral is convergent or divergent.

I) integral (cosx)^2*dx/1+x^2 a=1 b=infinte

since , we can compare to

II) integral dx/x+ e^2x a=1 b=infinte

since we can compare to

okay first one am okay with but will 1/e^2x converge as well?
o true doing the integral it will converge to 1/2e^-2 okay thanks!

Originally Posted by zangestu888

okay first one am okay with but will 1/e^2x converge as well?
o true doing the integral it will converge to 1/2e^-2 okay thanks!

that's right, you can work it out directly or note that we also have for , so another comparison would work