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Use the Divergence Theorem to compute the surface integral?

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2 Answers

By the Divergence Theorem,

the surface integral

= ∫[-1,1] dx∫[-1,1] dy ∫[-1,1] 3z^2 dz

= 2*2*z^3 from -1 to 1

= 2^3

= 8 <==Answer

Div F = 3z^2

 

∫∫ F ds  =   ∫∫∫ div F dV

∫∫ F ds = ∫∫∫ div F dx dy dz

           

            = ∫∫∫  dx dy 3z^2 dz

            =3∫∫∫dx dy z^2 dz.   The limits of integration for each integral is  -1 to 1.

            = 8