You can also use Stokes' theorem, or calculate the flux like you did.
Perhaps this topic may be of assistance, I did it in both ways there. If you still can't get it, I'll look into your problem.
Given is and they ask me to calculate the flux if
Where is in the up direction.
First I need to make a function who discripe the surface so thus
and and
If I calculate the cros product of the two I get then
Then the integral
Is this methode oké? if I calculate the integral I get and not
Who can help? Greets.
You can also use Stokes' theorem, or calculate the flux like you did.
Perhaps this topic may be of assistance, I did it in both ways there. If you still can't get it, I'll look into your problem.
It doesn't have a value, it's the nabla operator. It can be a gradient, a divergence or a curl - depening on how it is applied. Here, it is the cross product which gives the curl of the vector.
Edit: I just read your entire post: recheck your integral boundaries.
No, the curl (or the nabla operator on the vector via the cross product) doesn't mean the cross product of the vector with itself. Have you seen the curl yet? If not: do you even have to use it here? Check mathworld.com or wikipedia.com to see what the curl means