Evaluate the surface integral

for the given vector field

and the oriented surface S. In other words, find the flux of

across S. For closed surfaces, use the positive (outward orientation).

,

S consists of the paraboloid

,

and the disk

, y=1

I've thought about this for a bit, and I think it's a sideways half-circle with the base at y=1 and the apex at the origin. The correct answer is zero, I tried splitting it into two separate equations and adding their answers, which came out very nicely, but was not correct. I'm not sure how to set it up properly.