How Do You Apply the Divergence Theorem to a Non-Vector Field?

[craig16]

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..

 

[LCKurtz]

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..

Use the X² button above the advanced editing box for superscripts. Are you certain you have transcribed the problem correctly?

 

[craig16]

Yeah, I'm sure.
have you ever seen something like this?

 

[LCKurtz]

As it is written it is just a scalar surface integral which makes sense and can be evaluated. The reason I asked is your relevant equation: ∫∫_S F dS = ∫∫∫_B Div(F) dV isn't written correctly; it should be \iint_S \vec F \cdot d\vec S on the left. I just wondered if your original problem was mistranscribed. But, no, your original problem wouldn't have anything to do with the divergence theorem as it is written.

 

[craig16]

Which is why it makes me curious that they asked me to use the divergence theorem.
lol.. I dunno

 

[LCKurtz]

Which is why it makes me curious that they asked me to use the divergence theorem.
lol.. I dunno

I'm curious too. Why don't you ask your teacher and tell us what you find out?