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Use the Divergence Theorem to evaluate ∫ ∫ S F ⋅ d S where F=〈2x^3,2y^3,4z^3〉 and...

Use the Divergence Theorem to evaluate ∫ ∫ S F ⋅ d S where F=〈2x^3,2y^3,4z^3〉 and  S is the sphere x2+y2+z2=16 oriented by the outward normal.

Solutions

Expert Solution

According to divergence theorem

Now,

In spherical coordinates(as the surface is a sphere),

(As surface is a sphere of radius 4)

Let, , then   

Hence,

genius_generous answered 2 years ago
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