6. Integration and Accumulation of Change

Interpreting The Behavior Of Accumulation Functions Involving Area — Quiz

Test your understanding of interpreting the behavior of accumulation functions involving area with 5 practice questions.

Practice Questions

Question 1

Let $A(x)=\int_0^x f(t)\,dt$. What does $A(3)$ represent?

Question 2

Suppose $A(x)=\int_2^x f(t)\,dt$ and $f(t)>0$ on $[2,5]$. Which statement must be true on $[2,5]$?

Question 3

If $A(x)=\int_1^x f(t)\,dt$ and $f(x)=0$ at $x=c$, what is true about $A$ at $x=c$?

Question 4

Let $A(x)=\int_0^x f(t)\,dt$. If $f(t)$ is below the $x$-axis on $[0,4]$, what can be said about $A(4)$?

Question 5

Let $A(x)=\int_1^x f(t)\,dt$. If $f(t)$ changes from positive to negative at $x=c$, what behavior of $A$ is most likely at $x=c$?