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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:
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
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