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 $A(x)=\int_0^x f(t)\,dt$. If $f(t)>0$ for all $t$ between $0$ and $4$, what can be said about $A(x)$ on the interval $0\le x\le 4$?

Question 2

Suppose $A(x)=\int_2^x f(t)\,dt$. What is $A(2)$?

Question 3

If $A(x)=\int_1^x f(t)\,dt$ and $f(x)<0$ for $1<x<5$, what happens to $A(x)$ on $1<x<5$?

Question 4

Let $A(x)=\int_0^x f(t)\,dt$. If $f(x)$ changes from positive to negative at $x=3$, what happens to the graph of $A(x)$ at $x=3$?

Question 5

Let $A(x)=\int_0^x f(t)\,dt$ where $f(t)\ge 0$ for all $t$ and $f(t)=0$ only on a small interval. What does this tell you about $A(x)$?