Do My Improper Integral Solutions Converge or Diverge?

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Homework Help Overview

The discussion revolves around determining the convergence or divergence of two improper integrals involving the function 1/(2x^2 + x). The original poster seeks validation of their answers for the integrals from 1 to infinity and from 0 to 1.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the correctness of the original poster's conclusions and suggest that switching the answers might yield the correct results. There is a focus on finding upper or lower bounds for the integrals to determine convergence or divergence.

Discussion Status

The conversation is ongoing, with some participants providing feedback on the original poster's answers and others requesting to see the original work for comparison. There is an indication of productive dialogue as participants explore the reasoning behind the conclusions.

Contextual Notes

Participants note the importance of showing work to clarify misunderstandings and to validate the conclusions drawn about the integrals.

mat331760298
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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.
 
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If you switch your answers for a) and b), it's right.
 
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.
 
i don't see how the answers are opposite lol maybe someone can show me a) so i can compare to my work
 
mat331760298 said:
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.
 
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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