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Math Help - Surface Integral

  1. #1
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    Oct 2009
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    Surface Integral

    Evaluate the surface integral ∫∫ G(x,y,z) dS

    G(x,y,z) = x; S the portion of the cylinder z= 2 -x^2 in the first octant bounded by x= 0 , y = 0 , y = 4, z = 0
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  2. #2
    Senior Member
    Joined
    Jul 2006
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    Since you have z = f(x,y), parameterize the surface r(x,y) as

    \vec{r}(x,y)=(x,y,f(x,y))
    with
    0\le x\le \sqrt{2}, ~0\le  y \le 4, z \ge 0

    Then find dS = |r_x \times r_y|dx dy
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