Let $\mathbf { F } ( x , y , z ) = x y ^ { 2 } \mathbf { i }$

question 136

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x y ^ { 2 } \mathbf { i }$ and let S be the boundary surface of the solid $E = \{ ( x , y , z ) \mid 0 \leq x \leq 1,0 \leq y \leq 1,0 \leq z \leq 1 \}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

• A) \(0\)
• B) \(\frac { 1 } { 4 }\)
• C) \(\frac { 1 } { 3 }\)
• D) \(\frac { 1 } { 2 }\)
• E) \(\frac { 2 } { 3 }\)
• F)
• \(\frac { 3 } { 4 }\)
• G) \(1\)
• H) \(\frac { 3 } { 2 }\)

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