1. ## Surface Integral

edit: Solved

Evaluate the surface integral $\int \int_S \vec F \cdot d \vec S$ for the given vector field $\vec F$ and the oriented surface S. In other words, find the flux of $\vec F$ across S. For closed surfaces, use the positive (outward orientation).

$\vec F(x,y,z) = y \vec j - z \vec k$,
S consists of the paraboloid $y=x^2+z^2$, $0 \leq y \leq 1$
and the disk $x^2 + z^2 \leq 1$, 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.

2. Originally Posted by angel.white
Evaluate the surface integral $\int \int_S \vec F \cdot d \vec S$ for the given vector field $\vec F$ and the oriented surface S. In other words, find the flux of $\vec F$ across S. For closed surfaces, use the positive (outward orientation).

$\vec F(x,y,z) = y \vec j - z \vec k$,
S consists of the paraboloid $y=x^2+z^2$, $0 \leq y \leq 1$
and the disk $x^2 + z^2 \leq 1$, 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.
I got together with a guy in my class and we got this solved.