find-the-indicated-volumes-by-double-integration-the-volume-above-the-x-y-plane-below-the-surface--2

Question

Find the indicated volumes by double integration.
The volume above the $x y$ -plane, below the surface $z=x^{2}+y^{2}$ and inside the cylinder $x^{2}+y^{2}=4$

Carlos Pinilla · Accepted Answer

this region. But it is, uh, very nice visionaries between to parable Lloyds. So you have here, uh, one probable that is described by No, no, these are nice equation. Well, see, people do excess square. That&#x27;s why squared when the dealer part of a lawyer is warm. But as equation you swan, I want, like, these these iguanas equation, uh, citizen Isa, the lower part of Lloyd and then these other one? Yes, he has the same conclusion. No. See, she quinto excess square. That&#x27;s why, squirt. Why squared last one? So these monies on top is when is stop? I&#x27;m not money&#x27;s underwater bar. So we have that region and it is also inside off the ceiling. There, Over it is one that is very spiral. Put a C axes. So we&#x27;re gonna have some sort of like shape. But he&#x27;s so, like curves. So something like instead of like, uh, like these Yes, we want to find them. What is the volume of bad? And so what? We can do that in cylindrical See in Jericho also here he&#x27;s sexy score plus wise quantities r squared. So we would have these to be the top C is gonna be between our square blows. One. How are which is these part? This is because this is it, Um ce goes through X square, plus y squared. Plus one is in cylindrical coordinates. This is our square. Suarez Corp was one. That is it up on them is gonna be over these one buddies R squared. So that, uh, well, I&#x27;m the condition. Order volume is that, uh, the commission Is the businesses more than one not sealing their x square. Plus, why square? He says one of one. So what we could do is we could have that region. Here we have our see. So it&#x27;s gonna be became don&#x27;t stew and then have here r equals one is nine. I didn&#x27;t have that region then tilting the volume we rotate are on. All right, So why would go from zero? Oh, around 30. You ready there on fire? And I will go from 0 to 2 by So the internal, the volume he&#x27;s gonna be equal to or a cylindrical coordinates who do r B c you hard. So, uh, the scene is not reading r squared on r squared plus one on, uh, more well are those, uh, from Cyril of one, Because our so it&#x27;s positive on Thera goes all the way around here to bike. So that&#x27;s it. Do it first. So they drove off. See, there&#x27;s nothing here to present tonight is just gonna be you can do that separately, is gonna be here and follow it. Could meeting to buy 10 inches it will do to buy. So you have got ah, you&#x27;ll be able to buy. That was an angel from zero off one in Jobar Square. We&#x27;ll do our square does one So far this. See, we are so that, uh, well, when within acceptable to do is the general, you see? Well, you know they are That is a constant with respect to see she would be doing that within our square. That&#x27;s one of these people to, um Well, just the drill. Uh, this is just here between our square does one on our square. So these were the ableto r squared plus warm minus, But bottom part square to the stew council. And then we get very nice. We get that daddy&#x27;s with one so that these volume would be just equal to to buy Dana there was interest from zero off to one of our are. That was one you are on. The central is will be or to buy times our square hubs. Well, we could protein or a non zero so that this is gonna give us to buy time. So one square hubs, which is equal, though by, uh, So they drove these in trouble. These just FYI sequel to buy device.

Carlos Pinilla · Answer

So this region that he saw here three mutual space X R Why? See? So these regiones it&#x27;s Ah, there above the X Y plane money over there. I&#x27;m, uh, this below off these probable you buy. It&#x27;s Pamela V&#x27;s Z sequel to score plus y squared on the souls of all lying on the side of the ceiling there where he&#x27;s won along the sea axis. So it&#x27;s gonna be some originally these, so please feel these. So yeah, the ceiling there x squared plus y squared. There&#x27;s someone I&#x27;m, uh, do 3 a.m. planes equals zero. So Well, how do we find out what is volume? Um, so we did draw the sea axis on what should be here. They are squared the X square busboy squared. So these are is gonna go up to one, uh, my family like these when, uh, should be something like that. So we should be these region where this curve is. Uh, see, she&#x27;s going to r squared one. So that, uh, well, these can be seen us make our go from zero off the one Andi, not make your CEO at any point between zero on our square. So that these Bollywood B, You have to put a little turn with respectful data. Just, uh, these region ever dated, but these around our data uh, so that&#x27;s go for it. Uh, observing the way higher goes from zero of the one on the sea eagles. So that is our when see, goes from, uh, Cyril upto r squared. So where is the sea then? The bowline element Jacoby in is are So this is the volume room. Go ahead and do it dot We are voluntary. He&#x27;s respectable. Well, uh, see are this year do you have, uh, yeah, but so far, so yeah, uh, are deceived are on so Well, uh, this Federal Z Well, this is really just, uh, in trouble disease to see so that a volunteer routine are square zero. But we&#x27;ve just are square my No Ciro&#x27;s Or that was God. Well, things are not what&#x27;s in there Are these from zero to warm CEO to buy? Yeah, so, uh, uh, Well, uh, the central is our cube. You Joe bark, you br he&#x27;s are to the fourth or before, so we compute these within Syria. I wan is gonna be just 1/4 minus zero so far will be 1/4 of the Drover zero to buy. You think she&#x27;s bye? I&#x27;m glad we&#x27;re before is equal to my house. I have so that his own our volume there. These, uh, region is ball you. Oi! Close.

Carlos Pinilla · Answer

of this region. Three dimensional space X. Why? G So the region is, uh, above over. Plains equals zero on below. This Lloyd, he&#x27;s powerful, and he&#x27;s given by sea people do X squared plus y squared from the yesil Move off this plane. But this also inside of these ceiling there with these one are our little today. So these ceiling there was given by it was even by de questions. Um, that is excess square plus y squared. There&#x27;s someone, So I&#x27;m gonna have ah, this volume there. Ah, so it is. Uh see is between that on Sequels? You. So if you want to complete the volume Well Ah, but these are squared. This is, uh, square. So cylindrical Cory needs her soon vehicle. So? So that, uh, well, r z we draw the are with this big deal. See? So for this region, it&#x27;s gonna be like these where this is one to be, like, these families area on the irritate that area around. But for there, so where these curved is a burger Berries, huh? See people too r squared. So it&#x27;s about our Z through with these lines. See? He&#x27;s gonna bean. Do you um r squared. I&#x27;m r is between you on one side of this volume will be equal to the indigo, uh, or Karros all the way around your by arms from 01 the are on, uh, Z goes from ah syrup. Pilar squared serial R squared and in. That&#x27;s the accordion. Yeah. So the reading these Well, we&#x27;re doing the sea. So they developed. See just how easy with these volatile routine are square Once you we&#x27;ve turned this into going to ah Pedro Cruz, you to buy the interval from seal one off. Our hams are squared minus zero. So that doesn&#x27;t count Yaar. So these internal he&#x27;s neutral from zero to buy from zero warm off our cube. You are. You feel it on the wall in jail of our cubes. I do the floor by floor. This volatility in 10 Well, well, yeah. Also age Well from zero to buy you a beer. So this egregious that off 1/4 minute. Zero This is one. Pull 1 400 You know the drill from zip by Should be to buy. We&#x27;re waiting for Jesus by house. Sort of these values sequel to all right house

Carlos Pinilla · Answer

we have the following for a region you have here. Uh, a well, these. Why they You hear it? Eggs? No. Why the C axis? Now we have a region that he&#x27;s, uh yeah. With these has the upper bound to be these horrible Lloyds that, uh, this problem of years describe why? See, Sequel to X square plus white squared. And then the lower bound is this plane SI is equal to zero very nicely on that. And then some that is inside of the ceiling. There, over these one. I don&#x27;t have a searing. They&#x27;re here. What were these one? That? Ah, goods these So that we&#x27;re gonna be in a region like, uh, city shown there. So these, uh, region it&#x27;s called d you want to find what is the border? So I could do, um, cylindrical coordinates. See local where we blood here. Uh, see, when are the least turns to the C axis we know deserve these cuff? It has to be where these Where this is the the line articles One is a lot of this line, and we have these region this for this area on these, Uh, this is our bodies are square, so these would be the line. Uh, see, photo are square so that, uh, no, we have got to picture. And the meat with a daughter on feta. I feel pain nut. So, uh oh, where you get duties is that we could say We&#x27;ll see. It&#x27;s got everything. Zoo from R squared on dinner. Who are goes from zero of one. Are those friends. You have one. I&#x27;m, uh, moves all the way around. So all the way from zero to Dubai, get out will go between zero earned to buy. So these warrior would be equal to in cylindrical coordinates. So we&#x27;re gonna have our for the volume element. R D C. You are so ce goes with Dean Sear on r squared. Um, are those from Seo off? One in Florida was from Cyril up to buy. So first start. Well, we&#x27;re integrating the sea because there is this constant. So we just see evaluated between zero, um r squared. We should be Ah, squared er so eating it is here on r squared. This is gonna give us r squared with the Irish Square minus zero. She would have on our times r squared Diyar from zero off the one So have this intra go, Uh, which would be? Well, Leandro off our cube. So do you see in trouble? Uh, well, you should do are to the fourth power divided by four so that these, uh you can want zero. We just equal to 1/4 eso that this is gonna be 1/4. We&#x27;re getting dropped from 0 to 2 by, well, d theater. But these internal is just Ferre, but awaited meeting to buy zero times one floor for which we will do to buy my know Cyril the very by fours and of these councils and gives us for the NSA to there to buy helps. That is gonna be the volume there, boy. He&#x27;s, uh, High House.

Ahmed Kamel · Answer

in this question, the real being equal. Four triple integration off. He&#x27;s that Oh, the or deceit for integration limits me to be our poor school in the course to plus one Tzeitel and one zeal on boy over, she will make the first indication we get four bubble integration off our the or please eater which will be equally we take another integration to integration off ccta. And finally, if we take this integration, the final solution will be equal. Boy, Thank you.

Problem

Find the indicated volumes by double integration.…

Problem 22 Easy Difficulty

Find the indicated volumes by double integration.
The volume above the $x y$ -plane, below the surface $z=x^{2}+y^{2}$ and inside the cylinder $x^{2}+y^{2}=4$

Answer

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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