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Compute S(zi+xj+yk)dA\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A }

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Compute S(zi+xj+yk)dA\int _ { S } ( z \vec { i } + x \vec { j } + y \vec { k } ) \cdot \overrightarrow { d A } , where S is oriented in the positive j\vec { j } direction and given, for 0 \le s \le 1, 0 \le t \le 2, by x = s, y = t2, z =8 t.

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