Find the Average Value of the Function $f(t)=8 t \sin t^{2}$

question 34

Multiple Choice

Find the average value of the function $f(t) =8 t \sin t^{2}$ on the interval $[0, \sqrt{\pi}]$ .

• A) \(\frac{16}{\pi}\)
• B) \(\frac{8}{\pi}\)
• C) \(\frac{8}{\sqrt{\pi}}\)
• D) \(\frac{1}{\pi}\)
• E) \(\frac{16}{\sqrt{\pi}}\)

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Definitions:

Conditioning

The process of learning associations between environmental stimuli and behavioral responses, often distinguished as classical or operant conditioning.

Cognitive Components

The aspects of thinking and understanding, including perception, memory, judgment, and reasoning.

B.F. Skinner

An American psychologist and behaviorist who developed the theory of operant conditioning, emphasizing the consequences of behavior in shaping future actions.

Ivan Pavlov

A Russian physiologist known for his work in classical conditioning, particularly his experiments with dogs and salivation.