Surface area and line integral

1. Aug 26, 2012

rbwang1225

I met a proof problem that is as follows.
$\bf a = ∫_S d \bf a$, where S is the surface and $\bf a$is the vector area of it.
Please proof that $\bf a = \frac{1}2\oint \! \bf r \times d\bf l$, where integration is around the boundary line.

Any help would be very appreciated!

2. Aug 26, 2012

GarageDweller

Strokes theorem?

hmmm

Well say you perform a surface integral, if the vector field in question is the normal vector of the surface, then the only thing left in the integrand is dA (scalar).

So I guess using strokes theorem, you have to find a vector field who's curl is the normal vector of the surface.

Last edited: Aug 26, 2012
3. Aug 26, 2012

DonAntonio

Strokes Theorem is what we get sometimes from our loved ones. Stokes Theorem is, perhaps, what you mean.

DonAntonio

4. Aug 26, 2012

GarageDweller

Oops

5. Aug 26, 2012

chiro

What's this new theorem and who proved it lover boy?

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