# Math Help - Surface Integral

1. ## 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

2. 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 $dS = |r_x \times r_y|dx dy$