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## #1 2012-08-08 11:26:11

careless25
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### Integration

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:

## #2 2012-08-08 20:50:07

bob bundy
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### Re: Integration

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

## #3 2012-08-08 22:49:38

bobbym

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### Re: Integration

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #4 2012-08-09 02:56:48

careless25
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### Re: Integration

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 (2012-08-09 02:57:09)

## #5 2012-08-09 04:01:28

bob bundy
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### Re: Integration

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

## #6 2012-08-09 04:16:10

careless25
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### Re: Integration

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

Thanks Bob

## #7 2012-08-09 08:34:05

careless25
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### Re: Integration

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 (2012-08-09 09:25:31)

## #8 2012-08-09 09:52:18

careless25
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### Re: Integration

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 (2012-08-09 09:53:00)

## #9 2012-08-09 20:31:02

bob bundy
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### Re: Integration

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.

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