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Use the divergence theorem to find the total flux out of the solid x" +y < 9 , 0 < z < 1 , given that v(x,y,z) =xi+2yj+32k_108,b) 04136x18,None of the...

Question

Use the divergence theorem to find the total flux out of the solid x" +y < 9 , 0 < z < 1 , given that v(x,y,z) =xi+2yj+32k_108,b) 04136x18,None of these

Use the divergence theorem to find the total flux out of the solid x" +y < 9 , 0 < z < 1 , given that v(x,y,z) =xi+2yj+32k_ 108, b) 041 36x 18, None of these



Answers

Use the Divergence Theorem to evaluate the flux $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}.$
$$\begin{array}{l}{{F}(x, y, z)=\langle x+y, z, z-x\rangle, \mathcal{S} \text { is the boundary of the region be- }} \\ {\text { tween the paraboloid } z=9-x^{2}-y^{2} \text { and the } x y \text { -plane. }}\end{array}$$

I promise Reuniting using divergence serum. Alright, So calculate the creating of F which is partial of X. Ah, then d y d z dot with a function go through your plus one plus one which is you go to five. So then we have the volume integral five D V, which is just to go to five times V and then we calculate the volume of a quarter of a cylinder with radius one in height one. So it's gonna be five times a quarter of the volume which is pi r squared H supply one square times one medicals, five pi over four

All right. So from for their team, we've got a cube. Ah, two by two by two. And one by one by one. And we want to find the flux obtained by removing the cube, the small cube from the outer. All right, so then we dio following with the outer minus following with the inner and we plug in our Grady in of F we got three says could be three times the volume of the outer minus volume with dinner three times too cute. Minus one cubed that equals 21.

Right from 4. 12. So given the divergence serum confined the Grady of F like that ends at the volume and to grow using polar evaluating this integral, we get negative co sign Phi from zero to pi guthy tha from 0 to 2 pi and we get three are to the fifth over five from 0 to 1. This comes out to your 12 or five pi.

What shall we ever find these floods? Uh, office across the surface. Yeah. Thanks. That's great. That's white Jakob. Yeah. Game cap. Where's the rest of this year and so on like that for selling school? The humble towards experience or given on the questions are quite beginning A don't Yeah, not he I'm not. See? It's there. Let's for a moment. Next. Let's go back. Yeah, Biased from my high school. This sweat maybe. And with this using ordinary people. All right, that said, Mhm beat that. I don't even who find Uhh. It's either that save team go out there is going to happen. It's we have that said for it I'm I'm good with your hands. Big question away. Yeah.


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