Determine the surface integral for the surface S:...

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?
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    Answers ( 2 )

    1. mustafa nebio?lu
      mustafa nebio?lu
      As you say

      with 0 <= u and v <=1
      =
      It is correct!

    2. juho nevala
      juho nevala
      Thanks, only I don't understand why the integrals are takenfrom 0 to 1?
      (..0 to for du? and - to 1 for dv?)
      Why from 0 to 1? How do you determine the other boundary whenonly <= is given?

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