Mathematics: Verify that the divergence theorem is true for the vector field f on the region e. give the flux. f(x, y, z) = 2xi + xyj + 2xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.

Verify that the divergence theorem is true for the

Ответ:

bear342

05.01.2022

We have

$\mathrm{div}(\mathbf f)=\nabla\cdot\mathbf f=\dfrac{\partial(2x)}{\partial x}+\dfrac{\partial(xy)}{\partial y}+\dfrac{\partial(2xz)}{\partial z}=2+3x$

By the divergence theorem, the flux of $\mathbf f$ over the region $\mathcal S$ that bounds the region $\mathcal E$ is

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal E}\nabla\cdot\mathbf f\,\mathrm dV$

$=\displaystyle\int_{x=0}^{x=3}\int_{y=0}^{y=3}\int_{z=0}^{z=3}(3+2x)\,\mathrm dz\,\mathrm dy\,\mathrm dx$

$=\displaystyle3^2\int_{x=0}^{x=3}(3+2x)\,\mathrm dx=162$

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Ответ:

alizeleach0123

29.09.2022

Mathematics

hope this will help you

please mark me brain list pleas please

The width of a rectangle is 10cm less than the length. If the perimeter is 52, what

is the length a

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Verify that the divergence theorem is true for the vector field f on the region
e. give the flux. f(x, y, z) = 2xi + xyj + 2xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.

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