03 Jun 08
Hi all,
Since I've always found help here so far, I'll try again. I'm looking for:
lim (b-> infinity) Integral (0, b) ( Integral (0, b) (e^(-x(y+1)^2) ) dy) dx
As a matter of fact, I'd be happy enough if somebody could tell me the antiderivative (is that the correct word?) of e^(-x(y+1)^2) in regard to y... I seem to be a bit stuck here.
Thanks to anyone who can help 🙂
03 Jun 08
1 edit
Originally posted by angie88i heard it discussed on radio earlier today, it seems that most people aren't really interested in maths these days, when its mostly done by calculators and computers. hope that helps 😉
Hi all,
Since I've always found help here so far, I'll try again. I'm looking for:
lim (b-> infinity) Integral (0, b) ( Integral (0, b) (e^(-x(y+1)^2) ) dy) dx
As a matter of fact, I'd be happy enough if somebody could tell me the antiderivative (is that the correct word?) of e^(-x(y+1)^2) in regard to y... I seem to be a bit stuck here.
Thanks to anyone who can help 🙂
03 Jun 08
Originally posted by PalynkaThanks, but no... if you differentiate it, you have to differentiate the -1/[x(2y+1)] too 🙁 (And that's exactly where the problem lies).
The primitive of e^[-x(y+1)²] w.r.t. y is: -1/[x(2y+1)]*e^[-x(y+1)²]
(If you expand (y+1)²=y²+2y+1 it becomes evident why)
Aiko: ^ means "to the power of" (like x^2 = x²😉
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03 Jun 08
Originally posted by angie884,238
Hi all,
Since I've always found help here so far, I'll try again. I'm looking for:
lim (b-> infinity) Integral (0, b) ( Integral (0, b) (e^(-x(y+1)^2) ) dy) dx
As a matter of fact, I'd be happy enough if somebody could tell me the antiderivative (is that the correct word?) of e^(-x(y+1)^2) in regard to y... I seem to be a bit stuck here.
Thanks to anyone who can help 🙂
Maybe🙄
03 Jun 08
1 edit
Originally posted by angie88The integrand is positive (and [0, infinity) with Lebesgue measure is sigma-finite), so you can switch the order of integration, by Tonelli's theorem. You can integrate with respect to x easily, treating (y+1)^2 as a constant. Then take the limit as b --> infinity, to get:
Hi all,
Since I've always found help here so far, I'll try again. I'm looking for:
lim (b-> infinity) Integral (0, b) ( Integral (0, b) (e^(-x(y+1)^2) ) dy) dx
As a matter of fact, I'd be happy enough if somebody could tell me the antiderivative (is that the correct word?) of e^(-x(y+1)^2) in regard to y... I seem to be a bit stuck here.
Thanks to anyone who can help 🙂
Integral (0, b) Integral (0, b) (e^(-x(y+1)^2) ) dxdy = Integral (0, infinity) (y+1)^(-2) dy = 1.
EDIT Palynkster beat me to it.
03 Jun 08
Originally posted by angie88Keep throwing terms like antiderivative around and you'll end up having a stellar career in the financial world.
Hi all,
Since I've always found help here so far, I'll try again. I'm looking for:
lim (b-> infinity) Integral (0, b) ( Integral (0, b) (e^(-x(y+1)^2) ) dy) dx
As a matter of fact, I'd be happy enough if somebody could tell me the antiderivative (is that the correct word?) of e^(-x(y+1)^2) in regard to y... I seem to be a bit stuck here.
Thanks to anyone who can help 🙂