improper integral: converges/diverges before evaluation?

Hi. I'm a little confused about an issue in my homework problems involving improper integrals. I have problems like so:

Quote:

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

How do I determine whether it converges or diverges before actually evaluating it?

Re: improper integral: converges/diverges before evaluation?

Quote:

Originally Posted by

**infraRed** Hi. I'm a little confused about an issue in my homework problems involving improper integrals. I have problems like so:

How do I determine whether it converges or diverges before actually evaluating it?

What is the derivative of

Re: improper integral: converges/diverges before evaluation?

Re: improper integral: converges/diverges before evaluation?

Re: improper integral: converges/diverges before evaluation?

Quote:

Originally Posted by

**infraRed** ln(x)/x...?

So what that tell you about the integral and why?

Re: improper integral: converges/diverges before evaluation?

. But the integral of 1/x diverges, so the integral of the original function does too.