Math Is Fun Forum

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Question on improper integrals

Proof that

is divergent.

I know that in order to prove such a statement you'll first need to find

and show that the limit below does not exist:

However, I have difficulty integrating

at the first place

Last edited by coffeeking (2009-04-30 20:35:29)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Question on improper integrals

that's because it cannot be solved analytically

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coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Question on improper integrals

Hi luca, thanks for replying. Anyway since it cannot be solved analytically are there other method of proofing that it is divergent?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question on improper integrals

Hi coffeeking;

That integral from 0 to infinity can be done analytically( the answer wil be in terms of the gamma function) . It is ≈ .232. Concentrate on the integral from - infinity to 0. That one does not converge.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
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whatismath

Member

Registered: 2007-04-10

Posts: 19

Re: Question on improper integrals

I think we could use inequalities just to show the divergence:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question on improper integrals

Hi whatismath;

I know that

so we are covered there.

I think that you are right, we can use your inequality for -∞ to 0 and the whole problem is done.

Last edited by bobbym (2009-05-15 18:34:12)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Question on improper integrals

Hi, thanks for the input bobbym and whatismath, I appreciated it.