Evaluate this flux integral Please explain your answer I WIL

Evaluate this flux integral

Please explain your answer, I WILL FLAG AND NOT RATE if you just guess

Solution

The correct answer is 2) (256pi / 3). Use Divergence theorem. The divergence of the vector field is 1. So you are integrating 1 over the volume of sphere with radius 4 -> your answer is just the volume of sphere with radius 4 which is 4*pi*4^3/3=256pi/3. By Divergence Theorem the total flux through surface S is equal to total divergence over the volume that bounds this surface S. Hence the total flux is 256pi/3. Hope that helps.