3. A student was asked to calculate the surface integral of f(x, y, z) = 3xy over the plane z = 5 -x - y
3. A student was asked to calculate the surface integral of f(x, y, z) = 3xy over the plane z = 5 -x - y in the first octant. Their work is below but they made a mistake. Circle where the mistake happened and explain why it's wrong. f (x, y, z ) as S = f (x, y, 5 - x - y) V2 dA R 5- -y = v2 10 3xy dady = V2 3 (5 - y)2y dy 2 3V2 5 = 2 Jo 25y - 1092 + 3 dy . . . 625V2 = 8
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