Improper integrals

  • #1
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.
 

Answers and Replies

  • #2
Dick
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If you switch your answers for a) and b), it's right.
 
  • #3
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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.
 
  • #4
i dont see how the answers are opposite lol maybe someone can show me a) so i can compare to my work
 
  • #5
Dick
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i dont 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.
 
  • #6
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
 

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