# 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?