8. Applications of Integration

Using Accumulation Functions And Definite Integrals In Applied Contexts — Quiz

Test your understanding of using accumulation functions and definite integrals in applied contexts with 5 practice questions.

Practice Questions

Question 1

In an accumulation function $A(x)=\int_2^x f(t)\,dt$, what does $A(5)$ represent?

Question 2

A particle has velocity $v(t)=3$ for $0\le t\le 4$. What is the displacement of the particle on this interval?

Question 3

If $F(x)=\int_1^x g(t)\,dt$, what is $F'(x)$ according to the Fundamental Theorem of Calculus?

Question 4

Which expression gives the average value of a function $f$ on the interval $[a,b]$?

Question 5

A rate of water flow into a tank is given by $r(t)$ liters per minute. What does $\int_0^{10} r(t)\,dt$ represent?