Question

Use the Divergence Theorem to calculate the surface integral 

 
 
S
F · dS;

 that is, calculate the flux of F across S.

F(x, y, z) = (x3 + y3)i + (y3 + z3)j + (z3 + x3)k,

S is the sphere with center the origin and radius 2.
F dS; that is, calculate the flux of F across S.
Use the Divergence Theorem to calculate the surface integral
(x3 y3)i (y3 z3)j + (z3 + x3)k,
F(x, у, 2)
=
S is the sphere with center the origin and radius 2.

Image Transcription

F dS; that is, calculate the flux of F across S. Use the Divergence Theorem to calculate the surface integral (x3 y3)i (y3 z3)j + (z3 + x3)k, F(x, у, 2) = S is the sphere with center the origin and radius 2.

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