Use Differentials to Approximate the Arc Length of the Graph $\mathbf { P }$

question 35

Short Answer

Use differentials to approximate the arc length of the graph of the equation from $\mathbf { P }$ to $\mathbf { Q }$ . Round answer to four decimal places.
$$y = x ^ { 3 } + 3 ; \mathrm { P } ( 1,4 ) , \quad \mathrm { Q } ( 1.2,4.728 )$$

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Definitions:

Synaptic Cleft

The space between two neurons where neurotransmitters are released from one neuron to another.

Dopamine

A neurotransmitter involved in mood, motivation, reward, and the coordination of movement, playing a vital role in the brain's pleasure and reward system.

Serotonin

A neurotransmitter involved in the regulation of mood, anxiety, and happiness, among other physiological processes.

Norepinephrine

A neurotransmitter and hormone involved in the body's fight or flight response, affecting heart rate, blood pressure, and sugar metabolism.