5. Integral Calculus

Applications Of Integration — Quiz

Test your understanding of applications of integration with 5 practice questions.

Practice Questions

Question 1

If $f(x)$ is a rate of change, what does $\int_a^b f(x)\,dx$ usually represent?

Question 2

If $v(t)$ is velocity, what does $\int_{t_1}^{t_2} v(t)\,dt$ give?

Question 3

What is the average value of a function $f(x)$ on the interval $[a,b]$?

Question 4

If $\rho(x)$ is the linear density of a thin rod, what does $\int_a^b \rho(x)\,dx$ represent?

Question 5

A force $F(x)$ acts along a straight line. What does $\int_a^b F(x)\,dx$ represent?