Differential Area Element and surface integrals

  • #1
412
2

Main Question or Discussion Point

[SOLVED] Differential Area Element

While doing surface integrals, I am not sure as to which of the following is the correct differential area element to be considered:

i] [tex]dA = dx dy[/tex]

or

ii]
[tex]A = xy[/tex]

hence, using the product rule:

[tex]dA = xdy + ydx[/tex]
 

Answers and Replies

  • #2
45
0
The short answer is simply that [tex]dA = dxdy[/tex]

Your second equation does not make sense. To use the product rule, you have to differentiate A with respect to either x or y.
 
  • #3
107
0
the first one ... you always start with the infinitesimal element .

The short answer is simply that [tex]dA = dxdy[/tex]

Your second equation does not make sense. To use the product rule, you have to differentiate A with respect to either x or y.
that's not completely correct ..
if you start with [tex]A=xy[/tex] then [tex]dA=xdy+ydx[/tex] is lgeit .. but we always start with the infinitesimal element when we perform line , surface and volume integrals .
 
Last edited:
  • #4
412
2
thanks for the quick replies. I think I get it now...
 

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