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Lena [83]
3 years ago
9

Some come help me~ or ill fail this assesment~ u-u

Mathematics
2 answers:
posledela3 years ago
8 0
There is no image or question
sergiy2304 [10]3 years ago
5 0

Answer:

Thank you i will be taking these points now lol.

Step-by-step explanation:

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Find the outward flux of the vector field f=(x3,y3,z2) across the surface of the region that is enclosed by the circular cylinde
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Use the divergence theorem.

\mathbf f(x,y,z)=(x^3,y^3,z^3)\implies \nabla\cdot\mathbf f=3(x^2+y^2+z^2)

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\displaystyle\underbrace{\iint_{\partial\mathcal R}\mathbf f\cdot\mathrm d\mathbf S}_{\text{flux}}=\iiint_{\mathcal R}\nabla\cdot\mathbf f\,\mathrm dV

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\begin{cases}x=u\cos v\\y=u\sin v\\z=w\end{cases}\implies\mathrm dV=u\,\mathrm du\,\mathrm dv\,\mathrm dw

\displaystyle\iiint_{\mathcal R}\nabla\cdot\mathbf f\,\mathrm dV=3\int_{w=0}^{w=6}\int_{v=0}^{v=2\pi}\int_{u=0}^{u=8}(u^2\cos^2v+u^2\sin^2v+w^2)u\,\mathrm du\,\mathrm dv\,\mathrm dw
=6\pi\displaystyle\int_{w=0}^{w=6}\int_{u=0}^{u=8}(u^3+uw^2)\,\mathrm du\,\mathrm dw=50,688\pi
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PLEASE HELP &amp; SHOW WORK , ITS URGENT <br> it’s appreciated &lt;3 !!
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see if u understand the answer

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