967286…: “During the interesting raft”

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Let $F(x,y) = 2x+2y+2$ and $T$ be the triangle with vertices $(0,0)$ , $(1,0)$ , and $(0,1)$ . Set-up an iterated integral that computes the surface area of the surface $z=F(x,y)$ over $T$ . $\iint _T \d S = \int _{\answer {0}}^{\answer {1}} \int _{\answer {0}}^{\answer {1-x}} \answer {3}\d y \d x$

Compute the iterated integral above. $\iint _R \d S = \answer {3/2}$