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Vikentia [17]
3 years ago
9

Use the Divergence Theorem to calculate the surface integral

Physics
1 answer:
MrRa [10]3 years ago
3 0
Divergense theorem says flux across the closed surface = ∫∫∫ div F dV 

<span>div F = 3y^2+ 3 z^2 </span>
<span>convert to cylindrical </span>
<span>y = r cos t </span>
<span>z = r sin t </span>
<span>x = x </span>
<span>dx dy dz = r dx dr dt </span>

<span>∫ [0, 2pi]∫[0,3]∫ [-1,3] 3r^3 dx dr dt </span>

<span>2pi(3)(81/4)(4) </span>
<span>486pi
</span>
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The solution would be like this for this specific problem:

 

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