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Find the volume of the region cut from the solid sphere $\rho \leq a$ by the half-planes $\theta=0$ and $\theta=\pi / 6$ in the first octant.

$\frac{a^{3} \pi}{18}$

08:07

Carlos P.

Calculus 3

Chapter 15

Multiple Integrals

Section 7

Triple Integrals in Cylindrical and Spherical Coordinates

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Lectures

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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.

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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.

06:56

Sphere and half-planes Fin…

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Find the volume of the sma…

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Find the volume of the sol…

huh? On the following region First start. Didn't Yeah first, first opened. So that means that X y and C are positive. Positive? Um, we have last year over these e in the first stuff, country will book something sort of like that. And then we cut. Ah, so you have these regions, which she first doesn't, and then we cut cut through the place planes. Um, that, uh, physical zero on that is you look at bioware seeks so flavor seeks is gonna be a novel, like about Well, you have half a turn dairy. So by so that these should be by thirds equals toe by third's. And so five or six is gonna being about there. Explain. Very go sit by over six. So it should be with little Blake, uh, like these portion. So the the women would be what is inside the sphere Between these these range one. So well, for dad's, huh? You can see that, uh, Fada Yeah. Well, failure goes, uh, from Thera equal to Syria to ferret ical survivor six one being for if you he sang go feed goes up from vehicle zero. But he said this year actually looking up on, then I'll do the X axis. But he's, uh, the sex sexual with the fee goes to buy a house. So the Ranger Harvey is you can serum by halves. Sarah was between zero to your own bile by or six. So that or injury or volume can be computed us. Well, they drill. The thinner thinner goes from zero. The boiler seeks that he's you stay now or oh, figures from zero off by house. I've been rolled Those from Syria off a on the whole A melon is rose square. Sign off fee on a so well in the ring first. No squarely road. Lisa v ro cube thirds so dot of all waited between a zero is gonna be I just a cube thirds. Somebody's being bad. You read of the central. I'm being, uh, Well, no, we have She would have difficulty with people, too. You thirds. Ah, they drove from syrup to file or six off internal from zero to pi house. Wolf. Sign off. He the Fyvie. Sarah. So then drill sign. He's, uh, minus school sign. Um, because if you differentiate that you appreciate called minus course, you get sign. We respect toe So that even vehicle to minors. A cube, third central from zero to pi over six. Also, um Oh, sign off e treating by halves on zoo. But, um but he saw not so clear my house fly house once you're on daddy's. Well, then we helped into it the last interval after the Thera. So this number over here is gonna be local. Sign off playhouse. That is zero minus CO. Sign off zero cheese. All these because energy is 12 B minus one to minus minus with those two minuses. Cancel. And then we were gonna get originally tickle toe a cube thirds media from Siew up by over 60 was just 100 better. Which he's gonna people toe. You heard something them self era evaluated within five or six and zero. She's just gonna be able to five or six. So a cube third's them. So five or six on, uh, Logan, I want to play the stool. You also write us a by I'm saying Q divided by 18. She's three down six. So that is it. This is the volume

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