Determine the surface integral for the surface S: r(u,v) = (u, v, u^2 +v^2)

with 0 <= u and v <= 1

F(x,y,x) = (y,-x,z)

I assumed =

Calculated N = Ru x Rv = (-2u, -2v, 1)

F(r(u,v)) = (v, -u, u^2+v^2)

Now I get for the intergral (after some calculation):

If it's correct it's an easy integral, but I don't know theboundaries, 0 to for du? and - to 1 for dv?

Comments

## Answers ( 2 )

with 0 <= u and v <=1

It is correct!