Question

Evaluate the surface integral

S

F · dS

for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = −xi − yj + z³k,

S is the part of the cone z =

x2 + y2

between the planes

z = 1

and

z = 2

with downward orientation

Answer 1