receive a grade.

First the problem,

Let S be a closed surface given by x^4+y^4+z^4=1.

Evaluate

\(\displaystyle

\iint\limits_S {(\nabla \times F)} \bullet nd\sigma

\)

Where F=<2xy^2cosz,x+yze^z,xyz> and n is the outer normal.

Now my dilemma:

Using Stokes Theorem I believe I can evaluate as a line integral C or as a surface integral S.

My problem is with the parameterization.

The surface(x^4+y^4+z^4=1) looks similar to a cube but with rounded corners.

If I evaluate as a line integral then I am unsure of what parameters to use since this ( at least to me) is not a line I am used to defining. Unlike lets say, a circle, which can be parameterized as x=rcos, y=rsin.

Alternatively, if i try to evaluate as a surface integral then I think that to parameterize the position vector it would look something like

r=<x,y,(1-x^4-y^4)^1/4>.

This method begins to get complicated when I proceed to the next step and try to evaluate the cross product of dr/dx x dr/dy.

So, finally, I guess I question is-do I evaluate as a line or surface?

Also, how do parameterize this problem?

Any help is greatly appreciated.

Kid