Find the Length of the Curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 3 }$

question 46

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 3 }$ .
Select the correct answer.

• A) \(e ^ { 6 }\)
• B) \(e ^ { 3 }\)
• C) \(e ^ { 6 } + 2\)
• D) \(e ^ { 3 } + 2\)

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Definitions:

Positive Reinforcement

The process of encouraging or increasing a behavior by presenting a favorable outcome or reward upon the occurrence of the behavior.

Inventory Of Rewards

A catalog or list of rewards and incentives available within an organization, intended to motivate and acknowledge employee contributions.

Contingent Reinforcement

The provision of rewards or consequences based on the occurrence of a specific behavior, used as a strategy to increase or decrease that behavior.

Ethical Issues

Matters or situations that require a choice between right and wrong actions, often guided by moral principles.