Let

f(x, y, z) = z tan? 1(y2)i + z3 ln(x2 + 7)j + zk.

find the flux of f across s, the part of the paraboloid

x2 + y2 + z = 27

that lies above the plane

z = 2

and is oriented upward.

\int \int_{s}^{} f*ds

has divergence

If includes the disk which is contained in the paraboloid, then by the divergence theorem the flux is

If the disk is not part of , then subtract the flux of across the disk (with downward orientation; call it ). Parameterize by

where and , with normal vector

Then the flux of across is

which makes the flux across , .

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1