Find the Average Value of the Function F Over the Given

question 230

Multiple Choice

Find the average value of the function f over the given region.
- $f ( x , y ) = \frac { 1 } { x y }$ over the region bounded by $y = \frac { 1 } { x } , y = \frac { 2 } { x } , x = 2$ , and $x = 4$ .

• A) \(8 \ln 2\)
• B) \(\ln 2\)
• C) \(\frac { 1 } { 2 } \ln 2\)
• D) \(2 \ln 2\)

---

Definitions:

James-Lange Theory

A hypothesis that suggests emotions occur as a result of physiological responses to external events.

Autonomic Arousal

The activation or response of the autonomic nervous system to stimuli, resulting in physiological changes like heart rate, sweating, and blood pressure alterations, often associated with emotions or stress.

Subcortical Areas

Regions of the brain located below the cerebral cortex, involved in various functions including movement, sensory processing, and emotion regulation.

Temperament

Inherent aspects of an individual's personality, such as their tendency towards moodiness or calmness, which are often evident from infancy.