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Problem 55

Use the region $R$ with the indicated boundaries to evaluate each double integral.

$$\iint_{R} \frac{1}{y} d y d x ; \quad R$ bounded by $y=x, y=\frac{1}{x}, x=2$$

Answer

$4 \ln 2-2$

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## Discussion

## Video Transcript

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Why is the local so 20 minus one when executed zero whites go to zero when Wise could execute toe one wise goto one when wise when execute too two. Then why is go to two? No, Sorry. It's good to her. One over two because one over x. So this could talk. One about which is goingto 25. Good. So and very ill for X. There's untouched function. Which school? Executed to assist. Other question. So it's right to sketch this kind off function. Just get this burners and find that way. Are the boners off her, Huh? Here we have that. We kind of have one. Yeah, we can have to donate. To draw so many points is just to see Wayne. Um, the Here we have minus one and remind us too. They were gonna have a while. Here. We're gonna have to. This is a why this is the X saying sexiest, this door. Exit 12 Okay, this is here. We have minus one and minus two. So let's delight to skip the first function. We can sketch because excess kowtow to This is the type of function this one become show. It's like this one. This is what this is where X is good too. Two. Good. And the 2nd 1 is this one. Sketch it with food. Reds current. When we have minus two, we have also minus two Mr minus two exes. Go to minus two or four eye, which is so wait here when it's going to minus one extra two minus one. Have minus one. We just goto here. When you have zero, we have zero When it everyone, we have one here when you have to. We have to she and sit in Seoul, Seoul, where you would have the brine which is processing here. Good. So the time war is when we have minus two it's mine. I was to hear what has minus 0.25 minutes. That's somewhere. Hey, somewhere he are not sorry Menus The different girl. Which girl gonna use? Hey, free meals This warm somewhere here. And when it's good to minus one Is the release minus one somewhere here. So if he's going to 00 when remember that this is not the line because one over X when mixes good toe one or So we have a one when executed, too. Two. Here it has. Why not go to Which is go to 3.50 point five somewhere he So we have something like here, All right. I don't know. They're the parents, but what we need for us is intersection. So I mean, is that that section is here. We need are here. So what? He means that for this one, eggs is from one toe too. And why is from here toe here too? So are a cushion. You are integral is good to a particular signal rating with respect to X text exits from one toe a tour. Sorry on da Y's from one off too. Wanted wedding by two. We just got a little 0.5 on duh two. So we find our bronies friend our are so that we can do our integration. One over why this is we're in. We're found disses day, right? And the ex so far, so good this interval because it is very easy thing with because it's gonna be good to integral forms. One toe too. Congressional foot, One of our way. This is data to girl. Is that Aaron off. Why you just goto Aaron Natural rogard Timo. Why? Tenant board of violent ours. Which is tool one over to her, then deal Franks. This is good too. In a girl. Integral. From where? To Aaron. Off too. Eric. An off too minus. And the endless will have then dx You remember very aware that. Okay, this Aaron off, one of the two is cooked. Wearing off one minus. Aaron off too. So this and took off and take her from one it toe to Sorry. And a girl from 1 to 2 off. They're enough to minus Sorry. Minus air in off. One minus end off to in the express. Care enough to I can't afford to just keep steps. So is he mine? Us. This practice is Aaron minus one a in off one minus a n off too. I think this is a period there, homes. Here we have your four eggs. This is good too. And Tigger from one I would do off. This is too Ellen. Off to Minas. Ellen off 10 Plus Ellen off to this is to care enough to then D X fine. God have space here. Come. Area is destroyed. This is good too. Interviewer of Aaron to wear enough to his constant Mister, Just take off the eggs which is goingto eggs that we heard of two minute that we have to Aaron off two times x But except for wait too 1 to 2. You sit too. So this is good too. If we put very affects here is 22 minus one is one So it's going toe rogard team off too If you'll excuse You're very crater You can find the final for you which is good too One points three fades six two mine sword You see the answer for a Popara?

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