5. Calculus

Further Applications Of Integration — Quiz

Test your understanding of further applications of integration with 5 practice questions.

Practice Questions

Question 1

What does the area under a curve from $x = a$ to $x = b$ usually represent in integral calculus when the curve stays above the $x$-axis?

Question 2

If $F'(x) = f(x)$, what does the Fundamental Theorem of Calculus say about $\int_a^b f(x)\,dx$?

Question 3

Which quantity is most directly found by integrating a velocity function $v(t)$ over a time interval $[a,b]$?

Question 4

A function is continuous at $x = c$ if which condition is satisfied?

Question 5

What is the derivative of the accumulated area function $A(x) = \int_0^x f(t)\,dt$?