Mathematics: Find the area of the surface. the part of the cylinder y^2+z^2=9 that lies above the rectangle with vertices (0,,,2), and (4,2)

Find the area of the surface. the part of the cylinder

Ответ:

viktoria1198zz

13.03.2022

We can parameterize this part of the cylinder using

$\mathbf s(u,v)=\langleu,3\cos v,3\sin v\rangle$

with $0\le u\le4$ and $\cos^{-1}\dfrac23\le v\le\dfrac\pi2$ . Then the surface element is

$\mathrm d\mathbf S=\|\mathbf s_u\times\mathbf s_v\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=3\,\mathrm du\,\mathrm dv$

so the area is given by the surface integral, where

denotes the part of the cylinder in question,

$\displaystyle\iint_D\mathrm d\mathbf S=3\int_{v=\cos^{-1}(2/3)}^{v=\pi/2}\int_{u=0}^{u=4}\mathrm du\,\mathrm dv=6\pi$

Probably less work would involve a simpler geometric approach, but it doesn't hurt to practice setting up a proper surface integral.

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Ответ:

issagirl05

26.08.2020

Mathematics

5x^3-4x-1

Step-by-step explanation:

https://www.symbolab.com/solver/step-by-step/2x%5E%7B3%7D%2B4x-6%20%2B%203x%5E%7B3%7D-8x%2B7

I use symbolab, it's the best calculator for everything. Hope this helps!

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Find the area of the surface. the part of the cylinder y^2+z^2=9 that lies above the rectangle with vertices (0,,,2), and (4,2)

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