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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Definitions:

Method of Deduction

A logical process wherein one derives specific conclusions from general premises or known facts.

Ignoring

Deliberately paying no attention to something or someone.

Permissive-Indulgent

A parenting style characterized by high responsiveness but low demandingness, where parents are nurturing and accepting but provide few guidelines and rules.

Inductive Techniques

Methods based on observations used to arrive at general conclusions or theories.