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Find the indicated volumes by double integration.The first-octant volume under the plane $z=x+y$ and inside the cylinder $x^{2}+y^{2}=9$

Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 4

Double Integrals

Partial Derivatives

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So you have these region. But he's is described by Yeah, X Why c so reason region Very some. You know this purple. So So we each as equation nine minds X squared, minus minus X squared plus y squared. She want to see lead? Well, X y plane four. The excellent plane. Well, but is he will soon on the it also lies inside of these ceiling there or use one new d'oh in silently sitting there. So these, uh, that cylinder is he invited? Operation X Square. That's why Square a sequel to one two. What is that volume? Fine. What is that? A warning. So we'll do cylindrical quoting it Sounds of year, but he's not a square. When, uh, cultural advance for Z will be They're zero I that nine minus r squared yourself squared, uh, are approval from 0 to 1. Just one. There you go. Solely around from zero to buy. Well, so the whole turn both Okay, I gives us He's here. So he's running with the and the computer turning to go. Um So what are you have nine minus are square. That is the upper bone for C The lower on zero or are you? Goes from 0 to 1. So all these bounties that easy Is this the positive element? I was from Sue, Weren't Yeah, schools from Sirak by. So we do the central integrating the sea. Just something that I could see that would be the devil. You know, at this point, you're gonna have Ah, Then I get I'm not tense. You nine minus r squared. My mind is you know, so that would he, uh, because you weren't the center by the fit. So well, now we have two intervals giving trouble. Nine are Well, let's sit up. You know, Said you're being drill from Europe. The warm up mine are my listening to a bar Q because he's on our square. I'm sorry. So these year undying. Well, the General, these is, uh, nine spired squared lead role, that is, mines are to the four by four. What are these? Well into anything Lana zero use. Ah, nine house nine, house minus one for lines one or then minus that zero. She's austere square. Nice year or zero. Um, so we have that, uh, which commuted by Well ah, well, good bye. I'm making coming from in here. Four, We multiply this by two or two. So Well, a two minus one over four. She's 17. A team of 17 forks. But that's not everything. We have to go. He's right. Testa. Nah. Amazing to go. So after today, from here to Dubai. There. So, uh, the the volume we could totally drove around. You, too. Bye. These dean. Both, which, uh, is it legal to 17 forts times to buy the drill? Oh, the era. Just clutter. So that that followed? They didn't buy zero just by you. So Dubai armed, then, um, what about the still? Cancels want to there. So we have 17 ops. Bye. But he's, uh that is the volume of these on these fusion 17 i two.

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