S is part of the plan in first octante with orientation to down
Here's how to do it directly.
The surface can be parametrized by
The problem wants the normal vector pointing in the other direction, or
D is the region in the xy-plane bounded by the positive x and y axes and the line y = 1-x
The final final integral is then
[The surface can be written as z = 1 - x - y. So an obvious parametrization (at least to me) is (x, y, 1-x-y). It I had w = 1-x-y-z, then the parametrization would be (x, y, z, 1-x-y-z).can you please explain that for me in details how you parametrize like that
The stuff of mine you quoted has an error in it. The answer is not zero. I fixed it above.