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December 4th, 2011, 10:54 AM   #1
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ODE & Improper Integral

Can someone please help me with this integral ? I put F(K)= but I have problem with the F(0).
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December 4th, 2011, 10:55 AM   #2
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Re: ODE & Improper Integral

Sorry, I put F(k)= but I stuck everytime in F(0).
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December 4th, 2011, 02:04 PM   #3
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Re: ODE & Improper Integral

















because integrand goes to 0 at infinity + analytic function
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December 5th, 2011, 05:19 AM   #4
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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?
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December 5th, 2011, 06:29 AM   #5
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Re: ODE & Improper Integral

I think it should be


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December 5th, 2011, 06:45 AM   #6
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Re: ODE & Improper Integral

Quote:
Originally Posted by wnvl
I think it should be


Checked this ODE and the solution is indeed again .
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December 5th, 2011, 07:04 AM   #7
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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 .
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December 5th, 2011, 07:15 AM   #8
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Re: ODE & Improper Integral

Quote:
Originally Posted by talisman
why it should be where I did wrong to the integral? But mostly why ? if then the integral becomes which is not .
you made an error in the evaluation of for 0

concerning your second question, when the integrand is zero over the entire range of integration then the integral should be zero.
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December 5th, 2011, 07:44 AM   #9
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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.
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December 5th, 2011, 08:04 AM   #10
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Re: ODE & Improper Integral

Quote:
Originally Posted by talisman
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.




Quote:
Originally Posted by talisman
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.
For me this is trivial, but I don't have the background to give a strict proof.
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