Evaluate the surface integral Double 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 + (z^3)k,
S is the part of the cone
z = sqrt (x^2 + y^2)
between the planes
z = 1
and
z = 6
with downward orientation