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(a) find the spherical coordinate limits for the integral that calculates the volume of the given solid and then(b) evaluate the integral.The solid bounded below by the $x y$ -plane, on the sides by the sphere $\rho=2,$ and above by the cone $\phi=\pi / 3$

$\frac{8 \pi}{3}$

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

Johns Hopkins University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

04:18

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. The area above the x-axis adds to the total.

26:18

In mathematics, a double integral is an integral where the integrand is a function of two variables, and the integral is taken over some region in the Euclidean plane.

12:26

(a) find the spherical coo…

09:54

12:52

Compute the volume of the …

08:18

In Exercises $55-60,$ (a) …

17:33

Let $D$ be the region in t…

for the following volume. Um, he's, uh, or is a bounded between the corn. Um, by this commonly described by he eagles to my hurts between its very goldkorn needs. Very cool. It is. Above all, the next life plane explains this quite lately, saying that Zizek all did you on your side of the on this fear of really usedto So you would have something like that. Sort of like these region. No. So that is this fear of release to So what you say? I love that and also roll small them too. So you like to book you? What is the volume of these? These volume. So, uh, for feed you know that he's gonna meeting by thirds on the single. But I'm going there. Something equals to my house. So, uh, feel beating by thirds. Um, by hops on roll go from Syria to on, uh well, fair goes totally around. Were they not so the whole turn from zero off by two to play. So the volume is gonna be able to, um so fair goes from Jodi by buddies. The bombs 40. She goes from 5/3. I put my house. There is defeat on row goes from 0 to 2. You know, the Devil UMA Women Peace role Sign of feet. This is the volume element. So Marie melamine is very so you need a great, uh, it offers because nothing here depends on finish. He said, uh, from zero. Dubai is just gonna be equal to theta when we did to buy on a zero to would be able to just to buy So all of the central thing that movie go to to buy times drill from by thirds off by house. Oh, literal from 0 to 2 off road squared, sighing the row, the feet No. So, no, the reading throw room. You have no control. A rose clarity grow that would be able to roll cube thirds. So we are doing that. Taking too, and zero you don't pain to with their power hurts minus hero. So we'll be able to that. So we'll have that these people to to buy times Lewis there blower be very by three and then we help the last into Roland Girl from my third something by house Books Idol. He few room for the drill. A file sign draw sign where hes minus co sign Mine is close cause you view the friendship because with respectable See the thing you have fresh with minus call, Sign the pain sign. So, uh, you would be is regal toe these internally will do to buy them stew cube over three times, minus so close off by house, Myers cause by thirds I thirds. Uh, So who signed off my house? About zero. Dana. They have minus minus. So well, we just less well, that comes. We don't know what you're saying. Co signed off by thirds the sequel to together you circle your This is one, Then we'll by thirds. He's like these angle because, uh, he's, like, dividing how I turned out the spy into free free slices so that we're gonna have, like, one toe. So these families, 5/3 I'm doing well, it's cool signs. You will do 1/2. So this is one, uh, nice about, Of course. Why third's So these were the 1/2. So miners might as 1/2 of these 1/2 councils want to there. So you obtain that we should be gold miners. Why? No, that's positive. So good. You have ah positive number which we sure is a volume. So it's gonna be do. Their power comes by thirds. But did your thirties going toe eight eight by third's mom? So that should be It's about me life paid by thirds.

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