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math_proof Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits_{}^{}\int\limits_{}^{}e ^{xy}dA\]
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
where R is bounded by hyperbolas xy=1 and xy=4 and lines y/x=1 and y/x=3
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
dw:1353376012156:dw
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
dw:1353376473982:dw
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
can this be new region of integration?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large u=xy \quad v=\frac{y}{x}\] Making this substitution? Hmmm yah I think that will work out. Just need to get your substitutions in terms of x= and y= and then take the jacobian from there.
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
how did you get that u and v?
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
you just pick any that you want ?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
I chose u based on the integrand, it simplifies the exponential to something like e^u, which makes it a little easier to deal with. The v was based on the limits of integration, I'm not quite sure if i picked v correctly though :D i still need to check hehe
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
so use \[\int\limits_{1}^{3}\int\limits_{1}^{4}e ^{u}dudv\]
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Wellllll, if you change variables you have to multiply by the Jacobian as part of your change of differentials. It's a bit messy in this one also :\ hmm
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Do you happen to know what the right answer is suppose to be? XD I want to know if I'm on the right track here lol
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
i don't ;/
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Ok well I'll show you how I did it at least XD No promises that it's correct though lolol
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
oki thanks for your time
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Hmm so the Jacobian looks like this, it's the determinate of this matrix. When we change from dy dx to the other differentials, we have to multiply by this factor. \[\huge \left\begin{matrix}x_u & x_v \\ y_u & y_v\end{matrix}\right\]
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
In order to do so, we need our substitutions written in the form x= and y=
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Starting with this substitution, \[\large u=xy \quad v=\frac{y}{x}\]We'll move some stuff around to get x= and y=.
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large x=\frac{u}{y} \qquad y=vx\]
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large x=\frac{u}{(vx)} \qquad y=v\left(\frac{u}{y}\right)\]
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\large x=\sqrt{\frac{u}{v}} \qquad y=\sqrt{uv}\]
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
From there, we can apply the Jacobian. Taking the partials and placing them into the matrix.
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
wow thats gonna be messy
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\huge x_u = \frac{1}{2v \sqrt{\frac{u}{v}}}\] Yah they get pretty bad :( They clean up nicely though when you take the determinate :D
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
but the integrate will be the one that i wrote times the jocubian?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Yah, it'll be in this form \[\large \int\limits \int\limits e^{xy} dA \rightarrow \qquad \int\limits \int\limits e^u \left\begin{matrix}x_u & x_v \\ y_u & y_v\end{matrix}\right du dv\]
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
After calculating the Jacobian, I came up with\[\frac{1+v^2}{4v}\]I may have made mistakes somewhere though :D so make sure you try to do it!! I think it'll take too much time to show all the steps to get it though :3 Hopefully you have somewhat of an understanding of that thingy ma jigger :D
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
Keep in mind that you don't have to do the quotient or product rule on any of them, since they're only partials (one of the variables is held constant). Only messy chain rules :)
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
lol alright thanks a lot for ur help
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
\[\huge \int\limits_{u=1}^4 \int\limits_{v=1}^3e^u \frac{1+v^2}{4v}dv \;du\]\[=\huge \int\limits\limits_{u=1}^4 e^u \; du \int\limits\limits_{v=1}^3\frac{1+v^2}{4v} \; dv\]
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
so much homework
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
So I'm coming up with somethign like that D: pshh i dunno..
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
You have evil maf teacher too? :3 assigns bajillion problems? lol
 2 years ago

math_proof Group TitleBest ResponseYou've already chosen the best response.0
hmmm may be not billion but that kind of problems that take 2hrs to sold one like this one:p
 2 years ago
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