Math Help - Integral Divergence or Convergence Using Comparison Theorm

1. 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!

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

II) integral dx/x+ e^2x a=1 b=infinte
since $e^{2x} \gg x$ we can compare to $\int_1^\infty \frac 1{e^{2x}}~dx$

3. 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!

4. 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