December 4th, 2011, 11:54 AM  #1 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  ODE & Improper Integral
Can someone please help me with this integral ? I put F(K)= but I have problem with the F(0).

December 4th, 2011, 11:55 AM  #2 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  Re: ODE & Improper Integral
Sorry, I put F(k)= but I stuck everytime in F(0).

December 4th, 2011, 03:04 PM  #3 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: ODE & Improper Integral because integrand goes to 0 at infinity + analytic function 
December 5th, 2011, 06:19 AM  #4 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  Re: ODE & Improper Integral
I must solve the improper equation by using Ordinary Differential Equations, but I can't here is what I do: = = Thus: I solve the differential equation and then: to find I put and there I have problem. How I can solve the improper integral using ODE and If it can't be solved by using ODE how I can solve it using complex analysis? 
December 5th, 2011, 07:29 AM  #5 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: ODE & Improper Integral
I think it should be 
December 5th, 2011, 07:45 AM  #6  
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: ODE & Improper Integral Quote:
 
December 5th, 2011, 08:04 AM  #7 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  Re: ODE & Improper Integral
why it should be where I did wrong to the integral? But mostly why ? if then the integral becomes which is not .

December 5th, 2011, 08:15 AM  #8  
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: ODE & Improper Integral Quote:
concerning your second question, when the integrand is zero over the entire range of integration then the integral should be zero.  
December 5th, 2011, 08:44 AM  #9 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  Re: ODE & Improper Integral
Can you explain how I will find the ? and also why the integral of zero over the entire range of integration is zero? I asked 2 teachers in my university and told me that the integral of zero can not be defined.

December 5th, 2011, 09:04 AM  #10  
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: ODE & Improper Integral Quote:
Quote:
 

Tags 
improper, integral, ode 
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