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 $0 \leq x \leq 1$ .

---

Definitions:

Personal Dispositions

Inherent personality traits and tendencies that influence behavior and attitudes.

Prolonged Eye Gazing

A form of non-verbal communication that involves two individuals looking into each other's eyes for an extended period, which can intensify emotional connections.

Contraction of The Pupils

A physiological response where the pupils decrease in size, typically in response to increased light exposure or during focus on near objects.

Empathy

The skill of recognizing and sympathizing with another person's feelings.