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:

Producer Surplus

The difference between what producers are willing to accept for a good or service and what they actually receive in the market.

Consumer Surplus

The difference between what consumers are willing to pay for a good or service and what they actually pay, indicating the utility gained from the purchase.

Price Ceiling

A government-imposed limit on how high a price can be charged on a product or service.

Total Surplus

The sum of consumer surplus and producer surplus, representing the total net benefit to society from a market transaction.