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Se the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x2yi + xy2j + 5xyzk, s is the surface of the tetrahedron bounded by the planes x = 0, y = 0, z = 0, and x + 4y + z = 4. 1104 125​ incorrect: your answer is incorrect.

Respuesta :

LammettHash

[tex]f(x,y,z)=x^2y\,\vec\imath+xy^2\,\vec\jmath+5xyz\,\vec k[/tex]

[tex]\implies\nabla\cdot f=2xy+2xy+5xy=9xy[/tex]

The plane has intercepts in the [tex]x,y[/tex] plane at (4, 0, 0) and (0, 1, 0), so the flux is given by (via the divergence theorem)

[tex]\displaystyle\iint_Sf\cdot\mathrm dS=9\int_{x=0}^{x=4}\int_{y=0}^{y=1}\int_{z=0}^{z=4-x-4y}xy\,\mathrm dz\,\mathrm dy\,\mathrm dx=-48[/tex]

lhmarianateixeira

In this exercise we have to know about the divergent theorem and so using the given function calculate the flow through the integrals, in this way we will have to:

The flux is given by [tex]-48[/tex]

Knowing that the function is given by :

[tex]f(x, y, z) = x^2y+xy^2+5xyz[/tex]

Making the divergent function we will find that:

[tex]\nabla f = 2xy+2xy+5xy= 9xy[/tex]

The plane has intercepts in the xy plane at (4, 0, 0) and (0, 1, 0), so the flux is given by (via the divergence theorem):

[tex]\int\limits \int\limits_S{f} \, ds = 9 \int\limits^4_0 \int\limits^1_0 \int\limits^{4-x-4y}_0 {xy} \, dzdydx= -48[/tex]

See more about divergent at brainly.com/question/4890593

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