# another comparison thereom problem

• November 1st 2009, 01:04 PM
calcbeg
another comparison thereom problem
Hi

I am suppose to use the comparison thereom to determine if the following integral is convergent or divergent

integral sign (S) a= e and b= infinity (2010 + cos 2011 x)/ 2009x dx

these numbers are huge and I don't know where to start - especially with a cos in the middle of it.

Help!

Calculus beginner
• November 2nd 2009, 04:37 PM
Media_Man
$I=\int_0^\infty \frac{2010+\cos(2011x)}{2009x}dx$

The range for cosine is $[-1,1]$, so the numerator $N\in[2009,2011]$. The entire fraction $f(x)\in[\frac{1.001}x,\frac1x]$.

So, since $f(x)>\frac{1.001}x, I>\int_0^\infty\frac{1.001}{x}dx$. Can you get it from here?