Join our free STEM summer bootcamps taught by experts. Space is limited.Register Here 🏕

Oh no! Our educators are currently working hard solving this question.

In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics.



Numerade Educator



Problem 9 Easy Difficulty

Let $R$ be the region in the first quadrant of the $x y$ -plane bounded
by the hyperbolas $x y=1, x y=9$ and the lines $y=x, y=4 x$ .
Use the transformation $x=u / v, y=u v$ with $u>0$ and $v>0$
to rewrite
$$\iint_{R}\left(\sqrt{\frac{y}{x}}+\sqrt{x y}\right) d x d y$$
as an integral over an appropriate region $G$ in the $u v$ -plane. Then
evaluate the $u v$ -integral over $G .$


See explanation for result.


You must be signed in to discuss.

Video Transcript

{'transcript': "the problem is used given transformation to you want it? It's in bro. So our is a region In the first two Cordant founded by the lines line for two ax on y two three x and the pueblos ex wife one acts like one, two, three The transformation This accident to goto you over B. Why is it going to be so first? We have the region as his country. You the ugh this between one, two, three here from axes they got to you over there. Why is he going to be? We have you is equal to x counts live. So this is between one and three on the wise you two read So re is equal to why on DH from this to your questions were half. Why goingto ax And like the three AKs we have, we got you over a fee and the is equal to three times you over three half we squire. It's between you on three. You so if I scratch picture after written are the region are is this is you. One, two, three You're this isthe we square it for you be square. But you three You this part is a region off us. Then we compute the partially x Y, I assure you, which is equal to determinant of won over the conectiv. You over three square zero and one which is equal to one over so half and to grow. Is this going to into girl from one two, three into girl from Squire Mint of new too. Scored it Really you, Axel, I is use you camps one over me. Yeah, you. So which is it to you? One half you squire, From one to three crumbs. Now every from here first. This is a continent girl from wanted three You toms now one, two, three You over it A few you. Which is it now? In squatted to three tams. Well, half you square from one to three on three is or Tom's square it of three"}

Top Calculus 3 Educators
Lily A.

Johns Hopkins University

Anna Marie V.

Campbell University

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College