Several Variable Calculus

can anyone help me with the last question?

last part?

The "show that the volume of the hill is ..." part. This was originally part of a much longer question but the other parts were not relevant to this part

They are I think
we need the domain of the function.
I am assuming they are -inf to +inf in x and y

Okay here's the whole question

ok

have you worked out the jacobian?

mine is 3 (moded)

Yeah that's what I got too. I just got a bit stuck with the integral, I'm presuming it's easier to do it interms of u and v but I just can't see how

Okay here's the whole question

CORRECTION SORRY (I had a very busy day)

-9/4 u² - 9v²

definitely correct because at I got the correct answer at the end

Haha no bother, I just wolfram'd it because I got a different (and also wrong) answer than you did

So now I just split it up and integrate u and v respectively?

the answer in my last edit is definitely correct

then limits in u and v are unchanged

split the integral into two

need a simple substitution in both integrals

the one with exp(-9/4 u²) produces a 2/3 factor
the one with exp(-9 u²) produces a 1/3 factor
the jacobian is also 3

hence 2/3 * 1/3 * 3 * √π * √π = ... the answer

Ahh thanks I got it now! Out of interest why doesn't the limits change?