Divergence Theorem (F = -3xyi + 3x^2 j - 3yzk)

[Daniel_Feldman]

I need to evaluate:

F dS

Where F is the vector field F=-3xyi+3x^2j-3yzk

and the surface S is given by z=xe^(xy)

for x in [0,2] and y in [0,2]

Take S to have upward orientation.


My approach:

Use the divergence theorem.

divF=-6y

So then I set up the triple integral of -6ydzdxdy, with the bounds on x and y being 0 to 2, and the limits on z being 0 to xe^(xy). However, when I evaluated this I got -100.6687, which is not correct. Can anyone tell me what I'm doing wrong?

 

[Unco]

Numerically, I get about -215.6.

 

[Daniel_Feldman]

How did you solve it? Did you use the same approach I did?

The computer said that -215.6 is not correct either, so my only thinking was that I may have done something wrong on my calculator. I reintegrated using dzdydx (instead of dzdxdy), but again got -100.6687. I'm just wondering if maybe there's more to this than the divergence theorem, but am not sure.