Differential Area Element and surface integrals

[rohanprabhu]

[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] $$dA = dx dy$$

or

ii]
$$A = xy$$

hence, using the product rule:

$$dA = xdy + ydx$$

 

[CrazyIvan]

The short answer is simply that $$dA = dxdy$$

Your second equation does not make sense. To use the product rule, you have to differentiate A with respect to either x or y.

 

[mmzaj]

the first one ... you always start with the infinitesimal element .

The short answer is simply that $$dA = dxdy$$

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 $$A=xy$$ then $$dA=xdy+ydx$$ is lgeit .. but we always start with the infinitesimal element when we perform line , surface and volume integrals .

 

[rohanprabhu]

thanks for the quick replies. I think I get it now...