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Convert the integral$$\int_{-1}^{1} \int_{0}^{\sqrt{1-y}} \int_{0}^{x}\left(x^{2}+y^{2}\right) d z d x d y$$to an equivalent integral in cylindrical coordinates and evaluate the result.

Calculus 1 / AB

Calculus 3

Chapter 14

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

Integrals

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University of Michigan - Ann Arbor

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a full intro in Kardashian Kourtney's syndrome Using dropped from my one on one and each other from you hear the one minus squared off screwed of one liners White squirt on from zero X off X squared plus y squared. Oh, I see. This is about for C X, the ball for excess thes on the y That is about for why so, um like to turn it into our doing cylindrical ordinance are computed. So, uh, we have everything. First, how's that region look like? So we have Ah, something like these you have here z the X and the y axis. Seen that need Z goes because you're next so late you that is there not so strict plane seeing people to eggs It would be between the stools, abounded like that plane on being for X. You see, Iran, uh, squared bullsh, uh, one minus y squared so that we see that, uh, be square taxes. But I mean extra scores that so it is these region, but, uh, So this part of this circle, but for why? Beating miners one on one. So just God part. So the like, these region, she would be doing internal these this vision. So you say that, uh, circle on the plane. So we will get that is cylindrical. We should have our angle. Said, uh, he's gonna go from that angle up to that angle to be from more. It's cylindrical. Fair is gonna go meeting, uh, minus my house on, uh, buy a house, Onda. Uh, well, our radius goes from Syria off warm, because these, uh, I was trying to be instead of that. So our goes from zero after one on, uh, this convention. The conditions that are she is between sear on the X with legal access. You need to go card called Invisible to our course. Yeah. So these intro will be we'll turn you to the integral are more. See both within zero. I'm our course. Vera 36. Uh, these political coordinates was gonna be r squared on the these this part turning to our the sea we are because the volume element are and so, uh, are those from 0 to 1 from issue of Born on feta lose from rightness by house. My house minus by halves up by helps. So these is the internal. Very nice. Now, Um we go ahead on beauty. So, uh, well, firstly, interbreeding Z, but as a u z. So, uh, just evaluate in there with the reversible we have on our cube from there, being times are course, Vera. So you have that on being your integrating our You are the fair miss by halves up to my house. Oh, by house. So, uh, we do it here that we are the fourth. The trouble are to the fourth gr It's gonna be rto five new anyway. Five. You can see if you want to. Probably be Dean. 10 The birth. She's one minus you. So, um eso that is gonna give us, uh, one. We're fight times 1/5. Course later. Sarah the king, minus by house. Earn my house. Um, so the drill, of course. Science fair. Uh, the central physical tool shine. So it would be ableto Oh, see through sile by halves. She's having porn fever stems Sorry. By hubs. No minus no sign of Wales by house. From the look of our paragraph sign. So sign is like the something. Uh, my heart is going toe one, Simon. Thanks from the but minus Phi house with minors. One is mine. Is one there? No wonder. Said that, uh, is ableto one miners. Mine is one very like five should be going to to gives, um said that, uh oh, That should be already drill over five.

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