Use the Definition of Area as a Limit to Find $f ( x ) = 3 x ^ { 2 } + 2 x$

question 63

Essay

Use the definition of area as a limit to find the area of the region that lies under the graph of $f ( x ) = 3 x ^ { 2 } + 2 x$ over the interval $0 \leq x \leq 1$ .

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Definitions:

Corticobulbar

Pertaining to neural pathways that connect the cerebral cortex to the brainstem, involved in movement control.

Corticospinal

Pertaining to the motor pathways that travel from the cerebral cortex to the spinal cord, involved in voluntary movement control.

Direct Motor Pathways

Neural paths descending from the brain to the spinal cord responsible for the voluntary movement of muscles.

Sensory Adaptation

The process by which sensory receptors become less sensitive to constant stimuli over time, allowing organisms to focus on changes in their environment.