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Basic Vector Calculus question

N

Narmer

Diamond Member
If you have this: ??(???)dx=?(?'?'+??")dx=???'dn, Where the last integral is over the surface

Why do you have to integrate over dn instead of dx in the final integral, considering all the algebra was done in dx? I just did the calculations myself and I was wondering. Having taken vector calculus, I should know this, but I was wondering the basic reasoning.
 
I think they are using the divergence theorem where

?div(f)dv (volume integral) = ?f*dn (surface integral)

so
??(???)dx=?(???)dn = ???'dn

I'm assuming ? is a vector and ? is div otherwise it ends up taking the gradient of vector.
although more information would be nice. is the first itegral really just over x, the single dimension? does the integration over x and z happen to be just trivially 1?
 
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