PLZZ HELP 10 points!!!!!

Mathematics

2 answers:

Natali [406]3 years ago

8 0

The answer is 4.709, 4 7/9, 4.79

alex41 [277]3 years ago

5 0

I think its C thats what i put

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Evaluate the surface integral. s x ds, s is the triangular region with vertices (1, 0, 0), (0, −2, 0), and (0, 0, 12).

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Parameterize the surface by

$\mathbf r(s,t)=(1-s)(0,0,12)+s\bigg((1-t)(1,0,0)+t(0,-2,0)\bigg)$
$\implies\mathbf r(s,t)=(x(s,t),y(s,t),z(s,t))=(s-st,-2st,12-12s)$

where $(s,t)\in(0,1)\times(0,1)$ . We have

$\|\mathbf r_s\times\mathbf r_t\|=\|(1-t,-2t,-12)\times(-s,-2s,0)\|=2\sqrt{181}s$

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$\displaystyle\iint_Sx\,\mathrm dS=2\sqrt{181}\int_{s=0}^{s=1}\int_{t=0}^{t=1}s(s-st)\,\mathrm dt\,\mathrm ds$
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