If I had a region bounded by the surface $x^2 + y^2 = 9$ and a plane $x+y+z=1$, how would I determine what "boundary" I'd take the line integral over? Or would I take it over both boundaries?
The first being the circle of radius 3 with centre at the origin on the x-y plane
and the second, being the "ellipse-looking" boundary at the top (so the equation that comes out when we solve those two simultaneously)
?
Image of the region (so that small wedge above the x-y plane and below the surface plane): https://i.stack.imgur.com/sNdF9.png?
Website used: https://www.geogebra.org/3d
2026-03-28 08:40:07.1774687207
