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Let Rbe tnangular region in the zyplane wth vertices (C,0), (0,1), (2,L) and let the surface be the image Rin the graph : 1+3+2v' #tcan beshown that ILaas = [ ...

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Let Rbe tnangular region in the zyplane wth vertices (C,0), (0,1), (2,L) and let the surface be the image Rin the graph : 1+3+2v' #tcan beshown that ILaas = [ ["= f(s,u) drdy Determine f(x,y} ad enter cand un below s0 that equality holds - equan Abor integers (c not use derimal points) and d is a function of u (Enter yoUt answer fr d asy^2 6y OY | etc: DO nol Use spxes) Note the order Integration speoled on me RHS equaton (1}Use your ansier Ior _ {(2,9 Boove cetermare the surface area

Let Rbe tnangular region in the zyplane wth vertices (C,0), (0,1), (2,L) and let the surface be the image Rin the graph : 1+3+2v' #tcan beshown that ILaas = [ ["= f(s,u) drdy Determine f(x,y} ad enter cand un below s0 that equality holds - equan Abor integers (c not use derimal points) and d is a function of u (Enter yoUt answer fr d asy^2 6y OY | etc: DO nol Use spxes) Note the order Integration speoled on me RHS equaton (1} Use your ansier Ior _ {(2,9 Boove cetermare the surface area ot $, Enter your answer below using three deamal places Gunface 7meaol 8e



Answers

Set up and evaluate the indicated triple integral in the appropriate coordinate system. $\iiint_{0} z e^{\sqrt{x^{2}+y^{2}}} d V,$ where $Q$ is the region inside $x^{2}+y^{2}=4$ outside $x^{2}+y^{2}=1$ and between $z=0$ and $z=3$.

So we cut it? No bythe. So let's just get that looks on their life when I was feeling understood. Ah, something wrong? Yeah, very loose here, too. We have these things simply with a stroke. So that tells you pain. Yeah. Okay. Seriously, C squared something. And so it was the one. So get over it. This whole thing. Senior post minus one. Why? Or the service. But you can do Where's our well, something. Hm? Yeah, the Art Spiegelman. So that was pretty small. Yeah. So look. Okay, fine. Yeah, yeah. What happened in the conversation? Wrong? Well, in the position so well, he was expected. So she started a story. Excellent. Thank you. Know what it's called? Sign. Wow. One C course where? Pointing up here the next one scene projects. Uh huh. Yeah. There is no protection with acceptance. You know what Will you really? He seems very good. Coordinates spent called palm Second thing Question. Uh, yeah. What is the point? Point said the Yeah, going to it from that for science feed we owe you, right? Look at that. Yes, here from the cycle. You know, the things going on? Yeah. Yeah, Well, yeah, I'm down. Wow. Right. So this someone here in the second place business or there's money one so so that we can Yes. Okay. Oh, yeah. So these were here myself. It's conducting. Not so, for example. Okay, fine. You know, Times Square three, and, uh, this is murder, Mom. So that all right? Don't you want to be self assigning this? What e a anybody? So, um, 56 not in spite of 26 e learning offer is a one. Now, the problem is a lot better. Because I wanted was getting my order. So that's the one. So we got the money. Uh huh. Be 5.4. So excuse me. Before you could be something like six, but, um, to five points. So what now? We continue to do so the total loss, These reporters, the 12% off science minus person. Uh huh. Three times. Before what? Six. Too long? Uh, Z, yeah. Yeah, that's what they are. So nothing minus one minus minus the site, but six. So this our people yourself like it's hard. Mm. Mike, this might happen. You know, they will be like this. Um hmm. But that sort of Katrina mhm? Uh huh. Less? Um, it's quite often so. What? So many people before That's one plus e by. So we were able to for one plus, but I was like this with scandals, so that all right, one plus square with it.

Surface we have The coun that is described by C equals two times the square root four x squared plus y squared we want to consider is corn between you can see equals toe two on Sequels to six. So let's sketch that. So Yup. Here, the wine. The X on the C axis things is in three dimensional space in other three. Uh, this cone he's gonna look something like that following, So I calmly the there is symmetrical rotations respectively. Sango That revolves around, See? So you have this count on the recorded by the plane she goes to do, There's gonna be a playing, like there the plane, see, hostile to on the plane. Seen it goes to six is gonna be some somewhere higher. So there, huh? This plan C equals 26 that cuts in there. What? Yeah, c equals six. So the remaining shape is gonna be something like that. What do you use, like the piece of calm? Uh huh. But she looks something like that. Um, 200 piece. I want to find them or this shape for these. That is off the tongue. What is the area area? So I would like to do of our organization. So you can say, Well, uh, that's right. In terms of the Royals, will you be when they involved? Very simple. That's a X is equal to you. And then why he goes to be so in that way she would be equal to to square square plus B squared on. Since C is supposed to go between to 16 this means that, uh, square go u plus B was between two times this great of you. Square bliss squared off you square filled. The square has to be between two and six. So divided by two we get. But this would be speaking you square blocks the square squared off that a sweet between one and three. So in the movie plane became you on these the plane this represent nonetheless, where the hell Mary uses? He's one on the outrageous ease. Uh, Cliff. So it is their guy in his shape in the plane. Well, assuming that is a circle in this length or there is three, government is one. It would be this reason, you know, is it is your name this shop so well, it's called that region. These So what we need to do to compute area is to integrate inside off the the differential Bavaria. This differential very at the cinema is gonna be equal toe the norm off the cross. Parents off our the view with parts of the do you Univision. So, um well, recital his regionally that belongs in the you will be playing. So this thing, this is France product can be computed as they following determine of I G. Okay. And then we right along this role, our serve you. That's gonna be they live over. Abundance will be one. See you on the fashion off. See, with respect you and then four cars should be along that his role on his role. How long are your views along? Bad room. And then us would be along these roles. 01 um, partial of C would respect toe? No. So, what is this partial of sea with respect, Toe. You was gonna be partial off these. He can't be square with three squared plus b squared China over partial on these physical toe one or the So since they since the Barcelona, he's well, we'll have to there and then she's the police are half we get get one half square place square and then times the partial of U which do you So these two councils and then parcel of civil respect for you is gonna be to you over squared off you square plus B squared you on the none. Um well, the partial off. Likewise, the partial off city with respect to be it's gonna be too V over a squared off you square loss. It's good sure that all these this vector is gonna be equal to it's complete that very terms. It's gonna be high times this times that minus that times that's a minus. Partial oxy With this for two to you, there's gonna be minus j times too. You over the square root of you squared plus B squared funding for Jay you would have J. And so he stares at minus up things That's a minus bi shallow sea with respect to be that is that minus Also, this one was a long I You're minus j times that to be over the square root square must be squared. But in 14 is, uh, just K times one plus. Okay, so this is the normal This vector this better? The cross product is equal to that. So this it's norm is gonna people do the square root off that is squares you'll be Go square, you squared over that Squares are over you square has been squared plus about the square So squared again, square or square Let's be It's good on the plaza one so that these would be waas finding the one to review squared off so one would be medical infraction would use QuickBooks squared. Let me help. Well, the squares for four squared e Just one of you for you squared over you squared plus b squared. And so all these would be just five You squared plus b squared over you square waas the squared on square Root off that Which are these councils? Very nice. So these numbers is gonna be squared off. Fine. So that peace is ableto squared off five bu t v should at the area the area is equal to you could rate over Yeah, very handy in the U view plane. Square it off by Come see you. Mhm So we can pull loved. This is critical life. She's not the equals toe Expo The five. I was, uh, going to go over about vision be you visit. But this regionally is an analyst without a radius, please. I mean, a reduce one. Yeah, so that's regionally has area in the area of the region she called Thio. By times the outer reduces square soap items he squared minus the area of being a radius. The radius is one supply things one. So this with me by minus nine minus one that is eight and spoil. So this area is gonna be ableto five skirt of five temps things five or right? You know, in eight. Squared off five inspired. So that is the area. The area off this vision. The area off discount. Yeah. Hey, Dems, this growth of five by

For this problem would revalue its trip. Pointy girl, It is the TV where a curious the region are choosed the X Y plans and Pere breuder soon exact this. There's a parable. You what Along the x y plane. So this car buried as intersection please be ex wife fan. So the radios off this great circle is too. And there were looking for the region between years Para Boyd and uh um outside the sitting there. So this is a cylinder x squared plus y squared. Who's three? So we're looking for the region all Sanders sitting there and, uh, founded by this para brilliant and accepted. Also, we used the cylindrical coordinate system XY question are assigned her Why? Because they are assigned and Z close to see So we can re arrive this integral to go from 0 to 2 pi You fearful we talked 3 to 2 and the growth room a miner's ruutel four miles without square to zero. Ah, I can see to the the pc er you said which is untrue pie leading from route up 3 to 2. So the integrity of this line will be yourself very probably zero minus root up for later this hour Squares Fiat Sonu to be always this world ar minus top secret e minus Put up for minus house square yacht us Our first probably is really easy because they take curative it for this loins. Just one half Oscar. But for the second one. Um so this this please listen to through parts? No, you have more. Clearly. So the first one is just The first challenge is high a second path We treatise the substation. So the substitution Roy's let he was Teoh. Four writers are square to the what have which is the square root off this for man South square that a differential Peco's to one has four miners out square three minus my half camps Miners to our yard which is minus outcomes The first yard his pee pee tee coastal finals are Yeah, so we used this secu shin and this month so we can re arrived This you take right to just only for this part eating from 1 to 0, huh? He comes even if dynasty pt at the wake and years of divorce But parents to figure out the deteriorating for this one. But I just ride it out. Its Majesty. You couldn't find his team minus ET minus teeth and the value of that one. Ah. So the results tow you to the minus one minus one to combine me. Um, this this part we have financed, the issue will be high. Plus truth high times, twice a VT, minus part minus one, which is for hire you to give minus one minus pack. So this is the final solution to this program.


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