Use the divergence theorem to find the outward flux of the v

Use the divergence theorem to find the outward flux of the vector field F(x, y,z)= lx2i +2y2 j + 4z2 k across the boundary of the rectangular prism:

Solution

by divergence theorem, flux = triple integral(div F)dV div F = 2x + 4y + 8z now, flux = triple integral(2x + 4y + 8z)dxdydz = double integral ( 16 + 4(4y + 8z))dydz = integral ( 3(16+32z) + 8(9))dz = 3(48+72) + 48(9) = 792