Let ​ Use a Riemann Sum with Four Subintervals of Equal Length

question 45

Short Answer

Let ​
Use a Riemann sum with four subintervals of equal length to approximate the area of R (under the graph of f on the interval [0, 2]). Choose the representative points to be the left end points of the subintervals.
​
__________ sq units
​
Repeat previous part with eight subintervals of equal length .
​
__________ sq units
​
Compare the approximations obtained in previous parts with the exact area (12 sq units). Do the approximations improve with larger n?

---

Definitions:

Long-term Potentiation

Long-term potentiation is a long-lasting enhancement in signal transmission between neurons, believed to be a biological mechanism underlying learning and memory.

Implicit Memories

Memories that influence thoughts and behaviors without conscious awareness, such as skills and conditioned responses.

Mood-congruent Memory

The inclination to remember events that match one's present emotional state.

Emotional States

Refers to the complex psychological conditions that encompass the various feelings, thoughts, and physiological changes experienced by an individual.