Mathematics: Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = xyezi + xy2z3j − yezk, s is the surface of the box bounded by the coordinate plane and the planes x = 7, y = 2, and z = 1.

Use the divergence theorem to calculate the surface

Ответ:

Penelope9687

11.03.2022

By the divergence theorem, the surface integral of $\vec F$ across the closed surface is equal to the integral of the divergence of $\vec F$ over the region enclosed by .

The divergence of $\vec F$ is

$\nabla\cdot\vec F=ye^z+2xyz^3-ye^z=2xyz^3$

Then the flux of $\vec F$ across is

$\displaystyle\iiint_R(\nabla\cdot\vec F)\,\mathrm dV=\int_0^1\int_0^2\int_0^72xyz^3\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{\frac{49}2}$

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Ответ:

rickyop8010

26.05.2023

Mathematics

2x-10/4=3x

reduce fraction

2x-5/2=3x

2x-3x=-5/2

-x=-5/2

x= - 5/2

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Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = xyezi + xy2z3j − yezk, s is the surface of the box bounded by the coordinate plane and the planes x = 7, y = 2, and z = 1.

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