Verifying Stokes' Theorem: Am I Doing Anything Wrong?

[albertlee]

https://nrich.maths.org/discus/messages/27/147417.jpg

For the above problem, I simply take the curl of F and then take the cross product of it with the normal to the plane and integrate the whole thing with respect to the surface bounded by the plane.

Now, my solution is as followed with the help of computer program (save some manual calculation):

https://nrich.maths.org/discus/messages/27/147418.jpg

Now, why is my value negative? am I doing something opposite? I thought I take the right normal vector. My n ds = dr/dx cross with dr/dy multiplied by dx and dy = <1, 1/2, 1> dxdy

So, the whole (double) integration is just
curl of F dotted with <1,1/2,1> dydx where y goes from 0 to 8-2x and then x from 0 to 4.


please help

thanks

 

[albertlee]

never mind...

just figure out the -1/2 x of -1/2 x - yx should be +1/2 x.

ignore this thread then...