Find the outward flux of F(x, y, z) = 5x i + (y + 3)j + 8z² k across the unit cube in the first octant that has a vertex at the origin. A) 1 B) 0 C) 8 D) 9 E) 10

Question

Quizplus · Accepted Answer

The outward flux is calculated using the divergence theorem. The divergence of F is ∇·F = 5 + 1 + 16z = 6 + 16z. Integrating over the unit cube (0 ≤ x, y, z ≤ 1), the flux is ∫∫∫(6 + 16z) dV = 6 + 8 = 10.

Find the Outward Flux of F(x, Y, Z) = 5x