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#1 2012-08-07 13:26:11

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

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:

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#2 2012-08-07 22:50:07

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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

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#3 2012-08-08 00:49:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,031

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#4 2012-08-08 04:56:48

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

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 (2012-08-08 04:57:09)

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#5 2012-08-08 06:01:28

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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

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#6 2012-08-08 06:16:10

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

Re: Integration

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

Thanks Bob

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#7 2012-08-08 10:34:05

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

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 down. Any idea where I went wrong?

Thanks

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

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#8 2012-08-08 11:52:18

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

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 (2012-08-08 11:53:00)

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#9 2012-08-08 22:31:02

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,469

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.

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.  smile

Bob


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

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