5. Applications of Integrals

Average Value — Quiz

Test your understanding of average value with 5 practice questions.

Practice Questions

Question 1

Consider the function $f(x) = 3x^2$. What is the average value of this function over the interval $[1, 3]$?

Question 2

If the average value of a continuous function $g(x)$ over the interval $[0, 4]$ is 6, what is the value of $\int_{0}^{4} g(x) dx$?

Question 3

The temperature of a room in degrees Celsius is modeled by $T(t) = 20 + 5\sin(\frac{\pi}{12}t)$, where $t$ is the time in hours. What is the average temperature of the room over a 24-hour period (from $t=0$ to $t=24$)?

Question 4

A car's fuel consumption rate (in liters per hour) is given by $C(t) = 6 - 0.5t$ for $0 \le t \le 4$ hours. What is the average fuel consumption rate of the car during this 4-hour period?

Question 5

The height of a plant (in cm) is modeled by $h(t) = \sqrt{t} + 10$, where $t$ is in days. What is the average height of the plant over the first 9 days (from $t=0$ to $t=9$)?