AP Calculus BC : 8.1 Finding the Average Value of a Function on  an Interval- Exam Style questions with Answer- MCQ

Question

On a certain day, the temperature, in degrees Fahrenheit, in a small town t hours after midnight (t= 0) is modeled by the function \(g(t) = 65 − 8 sin (\frac{πt}{12})\) . What is the average temperature in the town between \(3 A.M. (t= 3)\) and \(6 A.M. (t= 6)\), in degrees Fahrenheit?

A \(57.609\)

B \(57.797\)

C \(58.172\)

D \(59.907\)

Answer/Explanation

 

Question

What is the average (mean) value of \(3t^{3}-t^{2}\)over the interval \(-1\leq t\leq 2\)?

(A)\(\frac{11}{4} \)           (B)\(\frac{7}{2}\)                 (C)8       (D)\(\frac{33}{4}\)                                     (E)16

Answer/Explanation

Ans:A

Question

The average (mean) value of \(\sqrt{x}\) over the interval \(0\leq x\leq 2\)
(A)\(\frac{1}{3}\sqrt{2}\)                   (B) \(\frac{1}{2}\sqrt{2}\)                  (C)\(\frac{2}{3}\sqrt{2}\)              (D) 1                   (E)\(\frac{4}{3}\sqrt{2}\)

Answer/Explanation

Ans:C 

Question 

The average value of \(\frac{1}{x}\) on the closed interval [1,3] is

(A)\(\frac{1}{2} \)            (B) \(\frac{2}{3}\)                   (C) \(\frac{ln 2}{2}\)                    (D) \(\frac{ln 3}{2}\)                           (E) ln 3

Answer/Explanation

Ans:D

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