Find the Length of the Curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 6 }$

question 112

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 6 }$ . Select the correct answer.

• A) \(e ^ { 12 }\)
• B) \(e ^ { 6 } + 5\)
• C) \(e ^ { 6 }\)
• D) \(e ^ { 12 } + 5\)

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Definitions:

Wernicke's Area

A region of the brain located in the temporal lobe, crucial for language comprehension.

Role

A function or position that an individual occupies in a social, relational, or organizational context, often defining expected behaviors and responsibilities.

Penfield Map

A representation of the motor cortex and sensory cortex in the human brain, illustrating the correspondence between body parts and their neurological representation, based on Wilder Penfield's research.

Speech Area

Regions in the brain, primarily located in the left hemisphere, involved in the processing and production of language.