Do My Improper Integral Solutions Converge or Diverge?

[mat331760298]

1. Determine whether the following diverges or converges. If converges, evaluate it.
a) integral from 1 to infinity of: 1/(2x^2 + x) dx
b) integral from 0 to 1 of: 1/(2x^2 + x) dx

I just want to check my answers. I got a) diverges and b) converges with value of ln|3/2|. Do these answers sound right? I would appreciate some feedback, thanks.

 

[Dick]

If you switch your answers for a) and b), it's right.

 

[gomunkul51]

You had a 50/50 chance and you blew it ;)

How did you got to your conclusions?

Basically you need to find an upper/lower bound (i.e. a simpler integral that you know how to evaluate) and show that the bound converges/diverges then the original integral also converges/diverges.

 

[mat331760298]

i don't see how the answers are opposite lol maybe someone can show me a) so i can compare to my work

 

[Dick]

i don't see how the answers are opposite lol maybe someone can show me a) so i can compare to my work

You haven't shown your work yet. If you do that maybe we can figure out what's wrong.

 

[mat331760298]

haha looked it over and when i did integration i had ln(x) + ln(2x+1) instead of ln(x) - ln(2x+1). makes sense now