Mathematics: Verify that the divergence theorem is true for the vector field f on the region e. f(x, y, z) = z, y, x , e is the solid ball x2 + y2 + z2 ≤ 64 for your answer, put in the flux across the boundary of e with respect to the outward normal.

Verify that the divergence theorem is true for

morganruhl2

11.01.2022

$\vec F(x,y,z)=\langle z,y,x\rangle$

has divergence 1, so by the divergence theorem, the flux of $\vec F$ across the boundary of is exactly the volume of ,

$\displaystyle\iiint_E\mathrm dV=\int_0^\pi\int_0^{2\pi}\int_0^8\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

or simply $\dfrac43\pi8^3=\boxed{\frac{2048\pi}3}$ .

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ernie27

21.01.2020

Look take a picture of your problem and will get the answer for u just like that within 3 seconds

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