# Integral Divergence or Convergence Using Comparison Theorm

• Feb 1st 2009, 01:40 PM
zangestu888
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

Help Much Appreciated!
• Feb 1st 2009, 01:46 PM
Jhevon
Here are some hints
Quote:

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 $0 \le \cos^2 x \le 1$, we can compare to $\int_1^\infty \frac 1{x^2}~dx$

Quote:

II) integral dx/x+ e^2x a=1 b=infinte
since $e^{2x} \gg x$ we can compare to $\int_1^\infty \frac 1{e^{2x}}~dx$
• Feb 1st 2009, 01:49 PM
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! :)
• Feb 1st 2009, 01:53 PM
Jhevon
Quote:

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 $\frac 1{e^{2x}} \le \frac 1{x^2}$ for $x \ge 1$, so another comparison would work