Q: Find the flux of F = (x, y, z) through the unit sphere (outward). By symmetry/divergence theorem: flux = triple integral of div F dV = triple integral of 3 dV = 3 times volume. Volume of unit ball = 4pi/3. Flux = 3 times 4pi/3 = 4pi. (Direct: on sphere n = (x,y,z), F dot n = x^2+y^2+z^2 = 1, integral of 1 dS = 4pi. Same!)