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# Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ). $$\int_{3}^{9} \int_{5}^{7}\left(\frac{x}{y}+\frac{y}{5}\right) d x d y$$

## 27.583

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##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

sort of. The problem we have here is said to a character trait. Durbar Antero Ah, Justice Deborah and single Front seat Tau nine 5 to 7 off Ex of Arai Plus why Divided by five deal for ext your performance. So this kind of integral remember that we we have the petition like this. This means that here we can put the protests here. Right? This one right. This storm sorry like so means that we can ever wait for us by with respect to the tow x the X and then with respect to do y it means that this dude bounds off eggs five 27 is that X's list is less than a seven and greeted in five. So this is they know Titian. Sorry. And can I have to? I will write it again. Don't worry on this is the X said d worry So is that the first in sugar? We can integrate this function we have here with respect to the X and in after it for waiting with very often eggs. Wait can me integrate? Where? For respect toe Why? So this is good too. We have this into a room from a 3 to 9 and so we can direct three. Integrate this one with respect to X means that we'll have excess square divided by two times excess squared, divided by two times one for right This one. So this is good too. Can I have this end table with respect? Toe eggs will have eggs too. Poor Have a program here writing. I have X the brook one of a to pull one plus one that is too poor, too ex. Too poor too. Divide by two times. Why is too why integrating this with respect to eggs? This is constant means that his press Why x y times X quiet tables and X then divide by five reintegrated ex Such excreta over too. Take it by ex thesis course 10th visit. We have X. So then all ever way Team in for death. The lower bound is full. No, it's five soaring. Aurora Brown is five. Yeah, because before five. And here we put seven. Then we are integrating with respect to d y now. Good. So far so good. So this is good too. Integrate some from city toe. Uh, nine. If we point it eggs here we have? If we put seven here, would have 47 47? Yes, you have 47 seven square eyes. Sorry. 49 was a seven square over two away and two Why? Then we put seven here we have plus Sitiveni. Why? Over five, five seven e Why then mine Us going to sub strapped If they're very of five here we have eggs. Great! That five square is 25 have 25 We went away then minus we pull five year. Where are five? Why? For the why Over five then. Then have this then D y sorry, Do you? Why Terrible, Right? Right here. So eso we heard this We were would be good to go and take over a vehicle so we haven't see Grew from taken from Ah Si Tau nine of who? So here we have 49 minus 25 over to why that 2049 minus 25 is 24 24 Divided by two is to work. You have to wear over. Why press you have seven? Why over five minus five awhile for five That is too. Why over fried plus two way over five toe over five. Sorry. This is of a five. You have five. Yeah, I have to. Why away our sin? Not very clear because they win too far. I'm both. I should have enough space here. So this is two way toe. Why over five in a variation. Yes. Anyway, this is a simple integral. Now it's not that bright girl. So you have to Ah, are so we're going to integrate with respect to why Justice? Easy. All right, 12 overrun. Integration off. 12. Arrive of respect or four. I mean, that is twere, if it's a great support integration off one of my wife, which is the co two pro Guaracy. Murph. All right, this is good, too. Toe wears time, Rosie. They're all guarded. Team that using natural gaiety off way here. We heard everybody don't have a lot of space here. Cameos do so on. This is good, too. Towards broke. We'll get you more for why Natural raw Garrity. And she was a natural girl. Tim Herron off. Why here? We have to weigh or five integration. This is equal to We have to remember that we have a Libra swap. What? Y two for one plus one is why square over too. Tour. We're so we have press Weiss crea over five. Then Variation is here. We have 39. This good too 90 here? Yeah, we have three. So we're going to refer to put their very off nine. Here we have here. We have no good tomorrow. Four million. So we have toward and off. Nine plus if we put 90 here with her 18 nine squares. Eight weren't soit worn over five, then minus. You have to wears. They're shreds. Reds tool. Very where toe. Where is just like this? Just a nice So where is it? Hello, Garrett, which used air in broker at small three. Then we put three here. We have minus nine over. Fight. So you guys more from nine. Remember that night Can be writing us three. Scratch it. So, Mr getting off this crowd is to locate him on three. So here we have 24 bro. That tomorrow? Three. This is good too. Twin for 24 0 guys, move three minus toe wear blow guys him off. Three minutes. That swears No God, you mouthy but that this is two times 12 24 24 minus two. Where is toward where? Blow guarded the way. The federal guide to all three. I swear, if they're a good team of three, we have 81 My last seven is 72. Press 72 uh, five. This is their own serviced world, bro. Get him off. Three. Press 7 to 2 or afraid if you want. You can use your car greater and then approximately. You can find 27 point five Rage. Yeah. Three. Again, Again. And go. So this is the truffle program. So it's good to 12 road. A team of three press 72 over fresh. Thank you very much. Just the tender.

##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp