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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 555

Hi,

I just had a calc final and one question stumped me. But i would really love to know the answer. Can anyone help me solve this?

I have to show that:

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

hi careless25

I'm getting a sign difference here, and I cannot see why ???

let

then

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,676

Hi Bob;

I'm getting a sign difference here, and I cannot see why ???

You could have chosen

as the factorization. Now the result follows.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 555

Thanks bob bundy and bobbym.

Following that we were asked to use that to solve

and told to use polar coordinates.

I was confused on how to go from the above function to a function of x and y.

*Last edited by careless25 (2012-08-08 04:57:09)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

Had me stuck too. But I found this:

http://en.wikipedia.org/wiki/Gaussian_integral

which looks like the thing for you.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 555

Hahaha I could not have thought of that on the final exam. Lost 10% right there .

Thanks Bob

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 555

Hi Bob bundy,

Can you verify my calculations below(just for my understanding):

now from here convert to polar co-ordinates

EDIT: I am not sure what the integration limits for theta would be...if it is 0 to pi/2, then this works out.

let u = r^2, du = 2rdr

since we squared the original equation, we square root the final answer so

This doesnt agree with what wolfram and wikipedia get . Any idea where I went wrong?

Thanks

*Last edited by careless25 (2012-08-08 11:25:31)*

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 555

I have been looking at this and I realized that if we just square the actual integral and dont use the fomula given to us, we get to the correct answer.

This does not work:

but this does:

*Last edited by careless25 (2012-08-08 11:53:00)*

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,393

hi careless25

This is getting beyond what I know but here's my thoughts:

The limits for theta would appear to be 0 to 2pi (a whole circle's worth ? )

The question asks for limits for x of 0 to infinity.

The Wiki proof goes from - inf to + inf.

So you'd need to half your answer.

That then agrees with the Wolfram answer

http://www.wolframalpha.com/input/?i=in … o+infinity

So I think you have done this correctly.

Did they really think you would dream that up under exam conditions? It's worth more than 10% if you can .. it's worth a 'first' !

What did other candidates do?

I can only think they were hoping you would have researched this in advance in which case it's an easy 10%

Oh well, it's done now. Fingers crossed for a good result.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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