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.