My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Thanks Tree3Thanks
  • 1 Post By v8archie
  • 1 Post By v8archie
  • 1 Post By v8archie
Reply
 
LinkBack Thread Tools Display Modes
October 29th, 2016, 10:05 AM   #1
Newbie
 
Joined: Oct 2016
From: italy

Posts: 9
Thanks: 0

Check if integral converges

Hi guys, I've to verify if $\displaystyle \int_{1}^{+\infty} \frac{e^{-x}}{\sqrt x}dx$ converges. I use the convergence criteria:
$\displaystyle \frac{e^{-x}}{\sqrt x} \leq \frac{1}{\sqrt x}$. The
exponent of $\displaystyle x$ is $\displaystyle 1/2$ , for the convergence criteria this integral should not converge, but standing to wolfram (and to the book) it does. What am I doing wrong?
nostradamus1915 is offline  
 
October 29th, 2016, 10:15 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,559
Thanks: 2148

Math Focus: Mainly analysis and algebra
The fact that your integrand is less than a divergent integrand tells you nothing.

You need to find a divergent integrand that is less than yours to prove divergence or a convergent integrand greater than yours to prove convergence. ($e^{-x}$).
Thanks from nostradamus1915
v8archie is online now  
October 29th, 2016, 11:37 AM   #3
Newbie
 
Joined: Oct 2016
From: italy

Posts: 9
Thanks: 0

So what should I do in this case?
nostradamus1915 is offline  
October 29th, 2016, 11:40 AM   #4
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,559
Thanks: 2148

Math Focus: Mainly analysis and algebra
Try some functions. If your first attempt has failed, try to find another.
Thanks from nostradamus1915

Last edited by v8archie; October 29th, 2016 at 12:06 PM.
v8archie is online now  
October 29th, 2016, 11:59 AM   #5
Newbie
 
Joined: Oct 2016
From: italy

Posts: 9
Thanks: 0

Wait, a convergent integrand greater than this is $\displaystyle e^{-x}$ !
p.s.: Oh you wrote that, didn't notice xD
nostradamus1915 is offline  
October 29th, 2016, 12:06 PM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 6,559
Thanks: 2148

Math Focus: Mainly analysis and algebra
Well done.
Thanks from nostradamus1915
v8archie is online now  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
check, converges, integral



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
How can I find whether the integral converges or not? tuphaan Calculus 2 March 22nd, 2016 06:20 PM
An integral converges into zero?!? OriaG Calculus 3 February 27th, 2013 11:24 AM
Finding alpha values for which an integral converges patient0 Calculus 4 May 30th, 2011 11:13 AM
Convergence of Sequence "{An^2} converges => {An} converges" cxc001 Calculus 3 September 9th, 2010 06:54 AM
prove integral of function converges IFF series converges? nedaiii Real Analysis 1 February 8th, 2009 08:15 PM





Copyright © 2017 My Math Forum. All rights reserved.