Verifying Stokes' Theorem on F, S in First Octant

[Moragor]

Homework Statement

Verify Stokes' Theorem for F and S
F=(y^2)i+(z^2)j+(x^2)k
S is the first octant portion of x+y+z=1

Homework Equations

The Attempt at a Solution

I know that it should be equal to -1 from Stoke's theorem, but I keep getting 1/4 when I use the normal surface integral way. (I have to do it both ways)

The integral I am using is
$$\iint x^2 + y^2 + (1-x-y)^2$$

What am I doing wrong?? :(

 

[Dick]

I don't think you took the curl of F before you dotted with dS.

 

[bsodmike]

“The line integral of $$\v{F}$$ around any closed contour C equals the surface integral (flux) of $$curl \v{F}$$ over any surface bounded by C

$$\oint_{C}\v{F}\bullet\v{dl}=\int_{S}\left(Curl\v{F}\right)\bullet\v{dS}$$

Found these in some of my old undergrad notes...