Compute the flux integral J. F . dA in two ways, directly and using the Divergence Theorem. S is the surface of the box with faces ( = 1,x = 3, y = 0, y = 2,= = 0, z = 3, closed and oriented outward, and F = 5x i + 5y?3 + 323k. Using the Divergence Theorem, Is F . dA = S. se S; dz dy dr = where a = 0 b= 3 0 2 P and q = X Next, calculating directly, we have J F - dA = (the sum of the flux through each of the six faces of the box). Calculating the flux through each face separately, we have: One = 3. J F . dA = S. S. dzdy = where a = 0 b 3 0 and d = 2 One = 1, J F . dA = Je Je de dy = where a = b = C = and d = Ony = 2. J F . dA = Jb S dz dx = where a = b = .C= and d Ony = 0. JSF . dA = S S. de dx = where a = b= C = and d = On z = 3. J F . dA = Sbry dy do = where a = b = . C= and d = And on z = 0. J F . dA = S Sy dy da = where a = . b = C= and d = Thus, summing these, we have J F . dA =