6. Integration and Accumulation of Change

The Fundamental Theorem Of Calculus And Accumulation Functions — Quiz

Test your understanding of the fundamental theorem of calculus and accumulation functions with 5 practice questions.

Practice Questions

Question 1

What does the Fundamental Theorem of Calculus say about the relationship between a derivative and an accumulation function?

Question 2

Let $A(x)=\int_2^x (t^2+1)\,dt$. What is $A'(x)$?

Question 3

What is $\frac{d}{dx}\left(\int_1^{x^3} \sin(t)\,dt\right)$?

Question 4

If $f$ is continuous and $F(x)=\int_0^x f(t)\,dt$, what is $F(0)$?

Question 5

What is the average value of a continuous function $f$ on $[a,b]$?