The discussion revolves around the application of the Divergence Theorem to a scalar surface integral involving the expression ∫∫S (8x + 10y + z²)dS, where S is defined as the sphere x² + y² + z² = 1. Participants are questioning the appropriateness of using the Divergence Theorem in this context, as the integral does not appear to involve a vector field.
The discussion is ongoing, with participants exploring the implications of the problem statement and questioning the validity of applying the Divergence Theorem as it is currently framed. There is no consensus reached, but the dialogue indicates a productive examination of the assumptions involved.
Participants note that the equation provided for the Divergence Theorem may not be applicable as it stands, leading to further questioning of the problem's requirements and the nature of the integral.
craig16 said:Homework Statement
Use the Divergence Theorem to evaluate ∫∫S (8x + 10y + z2)dS where S is the sphere x2 + y2 + z2 = 1.
Homework Equations
∫∫S F dS = ∫∫∫B Div(F) dV
The Attempt at a Solution
I dunno, this isn't a vector field so I don't know how to take the divergence of it so I can integrate..
craig16 said:Which is why it makes me curious that they asked me to use the divergence theorem.
lol.. I dunno