Use Stokes' Theorem to Evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$

question 76

Multiple Choice

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$ . $\mathbf { F } ( x , y , z ) = 6 x y \mathbf { i } + 5 y z \mathbf { j } + 2 z ^ { 2 } \mathbf { k }$ ; S is the part of the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ lying below the plane $z = 6$ and oriented with normal pointing downward.

• A) 0
• B) \(- 3\)
• C) \(3\)
• D) \(- 4\)

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Definitions:

Maintaining Social Order

Efforts or mechanisms put in place to ensure societal rules and norms are followed, allowing for stable, peaceful coexistence within a community.

Conventional Morality

A stage of moral development where individuals' behavior is shaped by conforming to society's norms and expectations.

Kohlberg's Stages

A theory proposed by Lawrence Kohlberg that outlines the stages of moral development individuals go through, from basic obedience to complex ethical and moral reasoning.

Conscience

An inner feeling or voice viewed as acting as a guide to the rightness or wrongness of one's behavior.