Use the Divergence Theorem to Evaluate $\iint_{S} \overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathrm{N}} d s$

question 69

Multiple Choice

Use the Divergence Theorem to evaluate $\iint_{S} \overrightarrow{\mathbf{F}} \cdot \overrightarrow{\mathrm{N}} d s$ Verify your answer by evaluating the integral as a triple integral.
$F ( x , y , z ) = 2 x \hat { \mathbf { i } } - 2 y \hat { \mathbf { j } } + z ^ { 2 } \hat { \mathbf { k } }$
$S$ : cube bounded by the planes $x = 0 , x = 2 , y = 0 , y = 2 , z = 0 , z = 2$

• A) 16
• B) 4
• C) 32
• D) 8
• E) 64

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