Let S Be the Part of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$

question 37

Essay

Let S be the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$ with x $\ge$ 0, y $\ge$ 0, z $\ge$ 0, oriented outward.Evaluate $\int _ { S } ( x z \vec { i } + 4 y z \vec { j } ) \cdot \vec { d A }$ .

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