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I'm working through some problems in a textbook and I wasn't sure how to do this

I have a function $f(x,y,z) = xyz$,and a region $S$ which is the triangle with vertices (3,0,0), (0,2,0) and (0,0,6) and I want to find the surface integral

$$\iint_S f(x,y,z) dS$$

I understand the theory behind this - I take two vectors in the region $S$, say (-3,2,0) and (-3,0,6) and find the cross product, which gives me a normal vector and then I parametrize $f(x,y,z)$ and integrate over $S$ which has bounds expressed in terms of my new coordinates.

I'm having trouble understanding how to paramatrize the region and the function - how do I do that?

Thanks.

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    The region is a part of the plane $\frac{x}3+\frac{y}2+\frac{z}6=1$ where $x,y,z\ge0$. One way to parametrize it is $\langle u,v,6-2u-3v\rangle$ where $0\le\frac{u}3\le1$ and $0\le\frac{v}2\le1-\frac{u}3$.2012-11-29

2 Answers 2