Use a fiNite Sum to Estimate the Average Value of the Function

question 51

Multiple Choice

Use a finite sum to estimate the average value of the function on the given interval by partitioning the interval and
evaluating the function at the midpoints of the subintervals.
- $f ( t ) = 1 - \left( \cos \frac { \pi t } { 2 } \right) ^ { 2 }$ on $[ 0,4 ]$ divided into 4 subintervals

• A) \(- \frac { 1 } { 4 }\)
• B) 1
• C) \(\frac { 1 - \sqrt { 2 } } { 2 }\)
• D) \(\frac { 1 } { 2 }\)

---

Definitions:

Serotonergic Neurons

Neurons that produce and release serotonin, a neurotransmitter important for regulating mood, appetite, and sleep, among other functions.

Drinking Coffee

Drinking Coffee involves consuming a beverage made from roasted coffee beans, which is popular worldwide for its stimulating effects due to caffeine content.

Stretching

The process of gently extending muscles to improve flexibility and range of motion.

Basic Rest-activity Cycle

A circadian rhythm concept suggesting that individuals have intrinsic cycles of rest and activity, notably proposed by sleep researcher Nathaniel Kleitman.