S is part of the plan in first octante with orientation to down
Here's how to do it directly.
Flux =
Let
The surface can be parametrized by
EDIT :
The problem wants the normal vector pointing in the other direction, or
then
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.