(5 points) Compute the flux integral F.n dS in two ways, directly and using the Divergence...

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(5 points) Compute the flux integral F.n dS in two ways, directly and using the Divergence Theorem. S is the surface of the box with faces x = 1, x = 3, y = 0, y = 2, z = 0, z = 3, closed and oriented outward, and F = 2x2 i+ 5y2} + 3z?k. Using the Divergence Theorem, SsF-ñds = dz dy dx = where a = b = ,d = ,p = and q = Next, calculating directly, we have , Fñ ds = (the sum of the flux through each of the six faces of the box). Calculating the flux through each face separately, we have: On x = 3, , F ñds = dz dy = where a = b = ,C = and d = On x = 1, F.n ds = [" (" dz dy = where a = b = C = and d = On y = 2, f, F ñ ds = [' S dz dx = where a = b = and d = On y = 0, F -ñ ds = dz dx = where a = ,b = ,C = and d = On z = 3, ,F i ds = S. S dy dx = where a = b = ,C = and d = And on z = 0, , F ñ ds = [ dy dx = where a = b = ,C = and d = Thus, summing these, we have F.ñ ds = (5 points) Compute the flux integral F.n dS in two ways, directly and using the Divergence Theorem. S is the surface of the box with faces x = 1, x = 3, y = 0, y = 2, z = 0, z = 3, closed and oriented outward, and F = 2x2 i+ 5y2} + 3z?k. Using the Divergence Theorem, SsF-ñds = dz dy dx = where a = b = ,d = ,p = and q = Next, calculating directly, we have , Fñ ds = (the sum of the flux through each of the six faces of the box). Calculating the flux through each face separately, we have: On x = 3, , F ñds = dz dy = where a = b = ,C = and d = On x = 1, F.n ds = [" (" dz dy = where a = b = C = and d = On y = 2, f, F ñ ds = [' S dz dx = where a = b = and d = On y = 0, F -ñ ds = dz dx = where a = ,b = ,C = and d = On z = 3, ,F i ds = S. S dy dx = where a = b = ,C = and d = And on z = 0, , F ñ ds = [ dy dx = where a = b = ,C = and d = Thus, summing these, we have F.ñ ds =