Determine whether converges or diverges. If it converges, evaluate the integral.

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- Nov 4th 2006, 07:49 AMFLTRDiverge or Converge
Determine whether converges or diverges. If it converges, evaluate the integral.

- Nov 4th 2006, 08:07 AMearboth
Hello,FLTR,

this is a standard integral which you probably know:

As you may know the arctan-function has the limit pi/2 if x approaches infinity:

and

So you get:

EB

Unfortunately the preview doesn't work properly. So I send you this post without checking. Please be careful, there might be some ugly mistakes! - Nov 4th 2006, 01:43 PMtopsquark
- Nov 4th 2006, 02:58 PMThePerfectHacker
Since,

Is continous on the entire number line, we well-define

At any point,

Choosing

Both the improper integrals converge to what Earboth said.