Math Help - Stokes' Theorem proof

1. Stokes' Theorem proof

Use Stokes' Theorem for the vector field c x r, where c is an arbitrary constant vector, to deduce that $\frac{1}{2}\oint_{C} r \times dr$ equals the vector area of any open surface bounded by the closed curve C, with the directions of dS and C related by a right-hand rule.

2. Re: Stokes' Theorem proof

Okay, what, exactly, does "Stoke's theorem" say? That would be good place to start.

3. Re: Stokes' Theorem proof

it says that $\int\int_{S} n \cdot (\nabla \times f) dS = \oint_{C} f \cdot dr$

i still don't understand how i can use that to solve my problem

4. Re: Stokes' Theorem proof

Good! But notice that your problem has the cross product with the line integral. You need to find a function, f(r), such that $f\cdot dr= ||r\times dr||$.

5. Re: Stokes' Theorem proof

im still incredibly stuck with this question! i dont even know what it is asking.