8. Applications of Integration

Finding The Area Between Curves Expressed As Functions Of X — Quiz

Test your understanding of finding the area between curves expressed as functions of x with 5 practice questions.

Practice Questions

Question 1

When finding the area between two curves written as functions of $x$, what should you subtract to get the vertical height of a typical slice?

Question 2

What is the area of the region between $y=x^2$ and $y=x$ on $[0,1]$?

Question 3

Why do you sometimes need to split the integral when finding the area between two curves expressed as functions of $x$?

Question 4

The curves $y=4$ and $y=x^2$ bound a region. If the interval of intersection is $[-2,2]$, what is the area of the region?

Question 5

Which integral gives the area between $y=\sin x$ and $y=\cos x$ on $\left[0,\frac{\pi}{4}\right]$?