Sketch the solid described by x 2 + y 2 ≤ z ≤ 1. use the divergence theorem to evaluate the surface integral over the boundary of that solid of the vector field −→f (x, y, z) = y −→ı + z −→ + xz −→k .

Looks like

The solid described by is the interior of the region bounded by the paraboloid and the plane . Call this region .

By the divergence theorem,

The divergence is

so that the surface integral reduces to

or in cylindrical coordinates,

true

step-by-step explanation:

where is the figure