Divergence Thm vs Stokes Thm: F=<z,-2x,xy>, S: z=4-x^2-y^2 above z=0; Find integrals
given F=<z,-2x,xy>
S: z=4-x^2-y^2 above z=0
Find integrals of F dot dS
I found the same problem here in this video https://www.youtube.com/watch?v=_ubpnd8F85g
The solution in the video is -8pi but when I applied the divergence theorem (integrals of divF dV), I got 0
divF=partial derivative with respect to x +partial derivative with respect to y+partial derivative with respect to z =0+0+0=0*Volume=0
Can someone please explain why the answers are different?
thanks
given F=<z,-2x,xy>
S: z=4-x^2-y^2 above z=0
Find integrals of F dot dS
I found the same problem here in this video https://www.youtube.com/watch?v=_ubpnd8F85g
The solution in the video is -8pi but when I applied the divergence theorem (integrals of divF dV), I got 0
divF=partial derivative with respect to x +partial derivative with respect to y+partial derivative with respect to z =0+0+0=0*Volume=0
Can someone please explain why the answers are different?
thanks