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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 $x^{2}+y^{2}=4$

Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 4

Double Integrals

Partial Derivatives

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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'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's why, squirt. Why squared last one? So these monies on top is when is stop? I'm not money'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're gonna have some sort of like shape. But he'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'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'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's gonna be became don't stew and then have here r equals one is nine. I didn'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'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's positive on Thera goes all the way around here to bike. So that's it. Do it first. So they drove off. See, there'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'll be able to buy. That was an angel from zero off one in Jobar Square. We'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'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'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.

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