Find each double integral over the rectangular region $R$ with the given boundaries. $$\iint \sqrt{x+y} d y d x ; \quad 1 \leq x \leq 3,0 \leq y \leq 1$$

we have a program here, It'd toe double integral again. So with two very Ambrose, it takes and way, way, way up. X is between one and three and X. Why is between zero and one? This is the temperature evil. This is gonna be good too. This is good too. Then Citigroup from you see the eggs because that's from one, 23 Again. Another table read Pootie in Prentice's from zero No. One. Scale it off Expressway. We can't even write Squared off express. Why? Why Expressway bore? Why no photo? This is good. I'm using a Titian for a run over to don't. And so do you, X. I'm sorry the way because we have to be very worried. Friends. Swifty, we've Bry, do I You know why? It's dish for me. Used this city I the y Then variation off eggs. So here the good way to ever win the descent. Several the press picked tow away is changer for free. Ables, let's say bridge leads right. A tea for your tea. Worry about T. Hey, quit too. Expressway expressway. And you see where if we differentiate tea with respect to away, I would have did T What would be a good toe the way? Because they freed. This is constant off. Why do I? One of the way and delivery and then the boners Here we have. Why? From a 0 to 1 means that tea will be good to hear from. If we put zero here means that is X. Why would he come here then? Eggs is less than or equal to t Beston already. Good too. We bought one here we have expressway, cause why the video for origin? All right. But you know, very forward is from 0 to 1. So mean that tea will be in this wrench from X press one president. Excuse me. The wreck This this dummy eggs press one. This case is a Okay, So, uh, good. So it means that I were a girl becomes This is good too. Harry. Go off from one, 23 both and a group from eggs. Toe Express one. Both This tea did to power one over two. Then did he De digs? This isn't not least, but they can't make it very, very level. This is T Tito. Poor one. Oh, uh, two. A big one. So this is going to We're going to grade from one, 23 You see Very where we use the formula's ready for me off K t tube. Okay, I know that if we have in Sago off T if you have a taper off, eggs begs to poor Okay, deal for eggs. This is Goto Eggs Tube. Okay, press one over. Okay, Press, see what we have her for me. If we have this press one his ex to park a press one defied k press one so means that he would have express Tito poor one over to press one, which is goingto 1243 over too. So here is and several off T. This is Tito Power. It's not a big tick t to power three over too. Over three over too. Then we pull the bone doors. Boner is expressed one. And here is the ex then indeed X. This is good. Tool are good if you put express one here, miss. That is integral. This is a country and cheaper from one for three on Sit too. Hi, party tomorrow. This is one from three. So we put express who are this is express one here. So is Xing. Press one, Boa three over two minus. This is the X eggs to boa three over two. Yeah, extra board. Three over two and horrors dividing by three. Over two. Then the eggs. Variation off picks. Good. This is good too. We used the same away. And this is express one's for your fix. Function of X. We can use this Samos here she is that we have to divide by. We have to toe out this exponents by one and divided by one. So here, this is good too. Express. One toe bore three over to press one is a five over too. So dividing five over too. But we can't put this Kia before apprentices that dividing three over two weekends put it to over three. Then press. There's no prices in mind. Us minus and trigger off this warren, is those eggs to party over to Is eggs to bore three over to press 15 over too then or over five over too. Then do ever a Russian we have to put is one in three. Well, your flex its form. 123 So this is good too. Wait. Put the value for three here. This is for okay, this is for minus one. That's the four minus two. Here we heard we can have this full over 15. It's gonna be good to fall over 15. Sorry. This is a 15 0 15 And that time, See, Or this one here. If we heard for this is for three plus one is full. Four is go toe to toe to so means that we have to borrow five times. The two of Otto is to tow bar five, which is goingto healthy to this. Is that too good here we have If we put eggs here Is exito bore five over too. Instead this is square it off, does it too? Minus clear it off. Asserted too. Yes. Good. Oh, uh too Yes. I put the furry off three years for this is treatable. I put here, Warren. Yeah, To two per five over too. You're a menace. You have to. And again, we're going to every weight with yes, here putting words. This is too a total bore. That's five two to par five over too. This is good too minus square. Load off. Five queer Oto because you have one. Press one here to square root of two to borrow. Five. There was a square with cheerful Sorry despair. Lot off 32. Good. It's not when I was confused, he every quote here is clear it off clean to par five. Don't use dissonant ation, miss better so that we can build off three to borrow five, then mine Us. This is clearly means that's press squealed off. One this one to provide for to expel the foreign disease. C one? Yeah. So far, so good on this. They're like their last chance, Iet's go to oh, if we're gonna make it, They're visible here. Don't have enough space. But if we add all this one is 11 15. Number 15. Yes. Won over 15. Just like I don't have enough space on the miracle we can have here stud. Two times for is held. Its That's too 100 32 minus. I don't know if I can read 100 tests to here. She's a pro prayer. Yeah. Good. Yes. So far so good. Good. Won over 15. Good. This is 132 minus Here. We can have 16 Scale it off too. Causes for spirit of two. Yeah. Yes. And then here is Touch six, Press 36. This is square root off today for this one. But it's not press because there is negative. Here I am. A change it This is the answer. Yeah, he has scaled off too. It's not Theresa poor. Where? Says 16 square lo tofu Two minus. That's six square. Looks up to you. This is the answer for aggression.

## Discussion

## Video Transcript

we have a program here, It'd toe double integral again. So with two very Ambrose, it takes and way, way, way up. X is between one and three and X. Why is between zero and one? This is the temperature evil. This is gonna be good too. This is good too. Then Citigroup from you see the eggs because that's from one, 23 Again. Another table read Pootie in Prentice's from zero No. One. Scale it off Expressway. We can't even write Squared off express. Why? Why Expressway bore? Why no photo? This is good. I'm using a Titian for a run over to don't. And so do you, X. I'm sorry the way because we have to be very worried. Friends. Swifty, we've Bry, do I You know why? It's dish for me. Used this city I the y Then variation off eggs. So here the good way to ever win the descent. Several the press picked tow away is changer for free. Ables, let's say bridge leads right. A tea for your tea. Worry about T. Hey, quit too. Expressway expressway. And you see where if we differentiate tea with respect to away, I would have did T What would be a good toe the way? Because they freed. This is constant off. Why do I? One of the way and delivery and then the boners Here we have. Why? From a 0 to 1 means that tea will be good to hear from. If we put zero here means that is X. Why would he come here then? Eggs is less than or equal to t Beston already. Good too. We bought one here we have expressway, cause why the video for origin? All right. But you know, very forward is from 0 to 1. So mean that tea will be in this wrench from X press one president. Excuse me. The wreck This this dummy eggs press one. This case is a Okay, So, uh, good. So it means that I were a girl becomes This is good too. Harry. Go off from one, 23 both and a group from eggs. Toe Express one. Both This tea did to power one over two. Then did he De digs? This isn't not least, but they can't make it very, very level. This is T Tito. Poor one. Oh, uh, two. A big one. So this is going to We're going to grade from one, 23 You see Very where we use the formula's ready for me off K t tube. Okay, I know that if we have in Sago off T if you have a taper off, eggs begs to poor Okay, deal for eggs. This is Goto Eggs Tube. Okay, press one over. Okay, Press, see what we have her for me. If we have this press one his ex to park a press one defied k press one so means that he would have express Tito poor one over to press one, which is goingto 1243 over too. So here is and several off T. This is Tito Power. It's not a big tick t to power three over too. Over three over too. Then we pull the bone doors. Boner is expressed one. And here is the ex then indeed X. This is good. Tool are good if you put express one here, miss. That is integral. This is a country and cheaper from one for three on Sit too. Hi, party tomorrow. This is one from three. So we put express who are this is express one here. So is Xing. Press one, Boa three over two minus. This is the X eggs to boa three over two. Yeah, extra board. Three over two and horrors dividing by three. Over two. Then the eggs. Variation off picks. Good. This is good too. We used the same away. And this is express one's for your fix. Function of X. We can use this Samos here she is that we have to divide by. We have to toe out this exponents by one and divided by one. So here, this is good too. Express. One toe bore three over to press one is a five over too. So dividing five over too. But we can't put this Kia before apprentices that dividing three over two weekends put it to over three. Then press. There's no prices in mind. Us minus and trigger off this warren, is those eggs to party over to Is eggs to bore three over to press 15 over too then or over five over too. Then do ever a Russian we have to put is one in three. Well, your flex its form. 123 So this is good too. Wait. Put the value for three here. This is for okay, this is for minus one. That's the four minus two. Here we heard we can have this full over 15. It's gonna be good to fall over 15. Sorry. This is a 15 0 15 And that time, See, Or this one here. If we heard for this is for three plus one is full. Four is go toe to toe to so means that we have to borrow five times. The two of Otto is to tow bar five, which is goingto healthy to this. Is that too good here we have If we put eggs here Is exito bore five over too. Instead this is square it off, does it too? Minus clear it off. Asserted too. Yes. Good. Oh, uh too Yes. I put the furry off three years for this is treatable. I put here, Warren. Yeah, To two per five over too. You're a menace. You have to. And again, we're going to every weight with yes, here putting words. This is too a total bore. That's five two to par five over too. This is good too minus square. Load off. Five queer Oto because you have one. Press one here to square root of two to borrow. Five. There was a square with cheerful Sorry despair. Lot off 32. Good. It's not when I was confused, he every quote here is clear it off clean to par five. Don't use dissonant ation, miss better so that we can build off three to borrow five, then mine Us. This is clearly means that's press squealed off. One this one to provide for to expel the foreign disease. C one? Yeah. So far, so good on this. They're like their last chance, Iet's go to oh, if we're gonna make it, They're visible here. Don't have enough space. But if we add all this one is 11 15. Number 15. Yes. Won over 15. Just like I don't have enough space on the miracle we can have here stud. Two times for is held. Its That's too 100 32 minus. I don't know if I can read 100 tests to here. She's a pro prayer. Yeah. Good. Yes. So far so good. Good. Won over 15. Good. This is 132 minus Here. We can have 16 Scale it off too. Causes for spirit of two. Yeah. Yes. And then here is Touch six, Press 36. This is square root off today for this one. But it's not press because there is negative. Here I am. A change it This is the answer. Yeah, he has scaled off too. It's not Theresa poor. Where? Says 16 square lo tofu Two minus. That's six square. Looks up to you. This is the answer for aggression.

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