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 a function $f$ that is continuous on $[a,b]$ and the accumulation function $F(x)=\int_a^x f(t)\,dt$?

Question 2

If $F(x)=\int_0^x (t^2+1)\,dt$, what is $F'(x)$?

Question 3

Which expression is the best interpretation of $\int_2^5 f(x)\,dx$?

Question 4

Let $G(x)=\int_1^x \cos(t)\,dt$. What is $G(1)$?

Question 5

If $F(x)=\int_3^x \sqrt{t+1}\,dt$, which statement is true?