In the interest of disclosure, this is a homework problem for which I will
receive a grade.
First the problem,
Let S be a closed surface given by x^4+y^4+z^4=1.
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
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.