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

]]>This does not work:

but this does:]]>

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

]]>Thanks Bob

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

which looks like the thing for you.

Bob

]]>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.

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

You could have chosen

as the factorization. Now the result follows.

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

let

then

Bob

]]>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: