Find the Average Value of F(x, Y, Z) Over the Given

question 166

Multiple Choice

Find the average value of F(x, y, z) over the given region.
- $F ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 }$ over the rectangular solid in the first octant bounded by the coordinate planes and the planes $x = 9 , y = 6 , z = 7$

• A) 88
• B) \(\frac { 166 } { 3 }\)
• C) \(\frac { 238 } { 3 }\)
• D) \(\frac { 328 } { 3 }\)

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Definitions:

Freudian Theory

A set of psychoanalytic theories developed by Sigmund Freud that emphasizes unconscious motivations and conflicts as drivers of human behavior.

Psychosexual Stage

A concept in Freudian psychology that describes the series of developmental phases children go through, during which the libido is focused on different areas of the body.

Milieu Therapy

A therapeutic approach that utilizes the environment, including people, setting, and activities, to influence a patient's behavior positively.

Social Behaviors

Actions or reactions of individuals in response to external stimuli, which occur in a social context or during interaction with others.