5. Calculus

Areas Between Curves — Quiz

Test your understanding of areas between curves with 5 practice questions.

Practice Questions

Question 1

What does the area between two curves on an interval represent when one curve is above the other?

Question 2

Which formula gives the area between $y=f(x)$ and $y=g(x)$ on $[a,b]$ when $f(x)\ge g(x)$ throughout the interval?

Question 3

If two curves cross inside an interval, what should be done to find the total area between them?

Question 4

Two curves intersect at $x=1$ and $x=4$. If $f(x)$ is above $g(x)$ on $[1,4]$, which integral gives the area between them?

Question 5

A student finds $\int_a^b \big(g(x)-f(x)\big)\,dx = -12$ for two curves with $g(x)$ above $f(x)$ on $[a,b]$. What is the area between the curves?