Find the Average Value of the Function Over the Region $f ( \varrho , \varphi , \theta ) = \varrho \cos \varphi$

question 330

Multiple Choice

Find the average value of the function over the region.
- $f ( \varrho , \varphi , \theta ) = \varrho \cos \varphi$ over the solid lower ball $\varrho \leq 8 , \pi / 2 \leq \varphi \leq \pi$

• A) \(\frac { 1 } { 3 }\)
• B) \(\frac { 3 } { 2 }\)
• C) \(- 3\)
• D) \(- 1024 \pi\)

---

Definitions:

Precipitate Depression

Depression that is rapidly triggered or worsened by specific events or situations, often characterized by a sudden onset.

Life Events

Significant occurrences in a person's life that can have profound effects on their psychological and emotional well-being.

Social Skills

The abilities necessary for successful social interaction and communication.

Expressed Emotion

A measure of the family environment that is based on how much criticism, hostility, and emotional over-involvement are directed towards the patient by family members.