5. Applications of Integrals

Area Between Curves — Quiz

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

Practice Questions

Question 1

When calculating the area between two curves, $f(x)$ and $g(x)$, over an interval $[a, b]$, what is the primary condition that must be met by the functions within that interval?

Question 2

To find the area between $y = x^2$ and $y = 4$ using integration with respect to $x$, what are the correct limits of integration?

Question 3

If $f(x) = 5 - x^2$ and $g(x) = 1$ over the interval $[-1, 1]$, what is the correct setup for the definite integral to find the area between these curves?

Question 4

Consider the region bounded by $x = y^2$ and $x = 2 - y$. Which variable should be used for integration to simplify the calculation of the area?

Question 5

What is the first step in determining the area between two curves, $y = f(x)$ and $y = g(x)$, when no specific interval is given?